What Is 10 Of – Full Guide: How to Use a Protractor Key Question: How do I measure an angle using a protractor?
Welcome to this free lesson to learn how to read a protractor and use it to measure angles.
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This complete guide to using Protractor includes several examples, animated mini-video lessons, free worksheets and answers.
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Before learning how to use a protractor to measure angles, let’s quickly review angle notation (understanding this important technique will make learning how to use a protractor much easier).
Angle notation: In geometry, an angle is denoted by the symbol ∠ and contains three consecutive letters representing the three points that make up the angle. The middle letter marks the vertex of the angle.
For example, notice in the diagram below that the two angles ∠ABD and ∠CBD have point B as their vertex, but have different measurements.
In this example, ∠ABD=120 and ∠CBD=60. But what if the angle measurement is not included in the diagram? How to find the angular measurement in such a situation?
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If so, watch this short animated video tutorial on naming angles before continuing with our protractor lesson.
Now that you know angle notation, you can learn how to use a protractor to measure angles.
First make sure you have correctly identified the angle. ∠MLN is the angle formed by M, L, N with vertex L. ∠MLNs are now colored in the diagram below. If coloring from an angle is helpful, you can use a marker or highlighter whenever you measure the angle of the paper using a protractor.
The next step is to align the center mark of the protractor to the vertex of the angle (point L in this example) as follows:
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Make sure the bottom radius of the angle (LN in this example) is aligned with the bottom of the protractor as shown.
Now that you have your protractor ready, the final step is to use it to determine your angle measurement.
We are trying to find a measure of ∠MLN. To do this, you need to determine where the upper ray of the angle (segment LM in this example) intersects the protractor, and then read the measurement.
We know that ∠MLN cannot be 120 degrees because it is an acute angle (less than 90 degrees).
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In Example D, ∠WYZ and ∠WYX are both right angles, so they are neither acute nor obtuse, both 90 degrees.
You may not have needed a protractor to determine that ∠WYZ and ∠WYX are right angles, but this example shows how a protractor can always help you find the measurement of a given angle.
Looking for more practice measuring angles using a protractor? Click the link below to download the free worksheet and answer sheet. You may have heard the term “10/40 window” from sermons or visiting missionaries, but you weren’t sure what the term actually meant or why it was important to you. It might seem like some kind of jargon only used by mission experts.
The 10/40 window is a rectangular geographic area stretching from North Africa through the Middle East to Asia, covering 68 countries.
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Its name comes from its location between 10 degrees and 40 degrees north latitude. Mission strategist Luis Bush and his wife, Doris, were looking for a way to explain the opportunity and need for people to hear about Jesus for the first time. I met and began to love and respect Luis and Doris Bush when they temporarily moved to Virginia in the mid-2000s to attend our local church. Luis said that Doris came up with the term “window” rather than her original name “10/40 box”. For Doris, the window gave her a better view of the important realities of her mission.
The Joshua Project, a Christian non-profit organization dedicated to gathering and disseminating information about minority groups with the least access to the gospel, estimates that the region is home to 5.11 billion people representing 8,717 distinct ethnic groups.
According to the Joshua Project, 68.6% of the Okna 10/40 people group (5,984) are considered unaffected, with a total population of 3.09 billion. This means that there are no thriving local church movements among these ethnic groups. Some of the world’s largest minorities yet to reach call this region home, such as Sheikhs, Yadava, Turks, Moroccan Arabs, Pashtuns, Jat and Burmese.
Download “How to Pray for the 10/40 Window” In most 10/40 windows there is little or no separation between religion and country.
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Western missionaries have long referred to this area as the “belt of resistance” because it contains most of the world’s Muslims, Hindus and Buddhists. Many governments in the region legally, economically and socially favor the dominant religion and actively suppress churches or persecute followers of Jesus. ANM receives weekly (sometimes daily) stories of such oppression and harassment from many of our 10/40 Window service partners.
The 10/40 window is where most of the world’s poor live. More than 8 out of 10 of the poorest people live in the 10/40 window. On average, they exist for less than a few hundred dollars per person per year. Most underachievers live in some of the poorest countries in the world, so it’s said that “poor people are lost and lost people are poor”. There are striking similarities between the world’s poorest and least evangelized countries.
Hear, my dear brothers, has not God chosen the poor of this world to be rich in faith and to inherit the kingdom he promised to those who love him? (James 2:5) Spiritual fortresses are built into Window 10/40.
Billions of people in the 10/40 window are trapped in spiritual fortresses that cause and sustain poverty, disease, and spiritual, political and religious oppression. These fortresses blind people to the transforming power of the gospel. Jesus identified himself with these poor and oppressed as he quoted the prophet Isaiah to mark the beginning of his own earthly ministry.
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The Spirit of the Lord is upon me, because he has anointed me to preach good news to the poor. (Luke 4:18-19)
Jesus explained in this verse that his mission, and therefore much of our mission, is to bring freedom and the light of the gospel to those who are oppressed and blinded by the strongholds of darkness and evil. This “recovery of sight” and “release” is a spiritual transformation seen in a 10/40 window.
For them the god of this world has blinded the minds of unbelievers, so that the light of the gospel of the glory of Christ may not shine, for Christ is the image of God. (2 Corinthians 4:4) Although we live in the flesh, we do not fight according to the flesh. The weapons of our warfare are not of the flesh, but the power of God to break down strongholds. (2 Corinthians 10:3-4) The Bible does not view these billions primarily as citizens of a state.
Rather, they are members of a “nation” (ethnos in ancient Greek), also called “tribes, peoples, and tongues” in the Bible.
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Then I saw a great multitude, which no one could number, from every nation, tribe, people and language, standing before the throne and before the Lamb, clothed in white and holding palm branches in their hands, crying out with a loud voice, “Salvation belongs to our God who sits on the throne, and to the Lamb!” (Revelation 7:9-10 ESV)
Therefore, when we look at mission assignments through Window 10/40, we see more clearly the numerous people groups, peoples, and languages God is calling to believe in Jesus Christ. Then we can better understand the strategic implications and necessity of obeying Christ’s command to make disciples of all nations.
Among the 68 strategic countries of the 10/40 window, ANM local missionaries are actively serving, evangelizing, and planting churches in 40 countries. In most cases, only believers and ministers in or near these countries have access to those who have not reached Window 10/40.
At ANM, we thank Luis and Doris Bush for their godsend and their vision for the 10/40 window. Their vision has helped us focus on our vision. By navigating this portal, we can better see and engage with the world’s tremendous needs and extraordinary opportunities for:
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