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Find the corret measure of 6

Find the corret measure of 6-example-1
User WJS
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1 Answer

5 votes

Answer:

∠3 = 102°

Explanation:

║A straight line always equals 180°. So all we need to do is subtract 78° ║from 180° for the missing angle.

180 − 78 = 102

∠3 = 102°

Further explanation:

║The image shows two slanted lines across one vertical line. If we visualize ║a circle around the point where the slanted line intercepts with the vertical ║line, we can solve this.

[we only need one line to work with, because both lines are parallel]

║That circle you visualized divides the intercept into four sectors. One of ║those sectors, or angles, is labled 78°. We need to find the angle measure ║underneath the labled sector. The sector in the bottom right corner has ║the same angle measure as the labled sector, which is 78°. The sector ║labled ∠3 has the same angle measure as the sector in the upper right.

[a full rotation around an angle is always 360°]

║This can be easily solved by subtracting 78° from 180° to get the angle ║measure for the upper right sector, which is equivalent to ∠3. Using basic ║subtraction, 180° − 78° = 102°. We can prove this by multiplying 78° by 2, ║multiplying 102° by two, and adding the products.

78 ⋅ 2 = 156

102 ⋅ 2 = 204

204 + 156 = 360

║Because the sums equal 360°, we can determine the answer is true.

User Jieter
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