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find the measure of all labeled angles in the diagram

Find The Measure Of All Labeled Angles In The Diagram class=

Sagot :

Answer:

∠1 = 127°

∠2 = 53°

∠3 = 127°

∠4 = 37°

∠5 = 53°

∠6 = 90°

∠7 = 37°

∠8 = 143°

∠9 = 37°

∠10 = 143°

Explanation:

If two angles form a straight line, they add to 180°, so ∠1, ∠2, and ∠3 can be calculated as:

∠1 = 180 - 53 = 127°

∠2 = 180 - ∠1 = 180 - 127 = 53°

∠3 = 180 - 53 = 127°

Then, ∠5 is corresponding to 53° because they are in the same relative position. It means that these angles have the same measure, so:

∠5 = 53°

On the other hand, ∠6 is opposite to the right angle, so it has the same measure, then:

∠6 = 90°

∠4, ∠5, and ∠6, form a straight line, so:

∠4 = 180 - ∠5 - ∠6

∠4 = 180 - 53 - 90

∠4 = 37°

Finally, the sum of the interior angles of a triangle is also 180°, so the measure ∠7 will be equal to:

∠7 = 180 - ∠2 - ∠6

∠7 = 180 - 53 - 90

∠7 = 37°

So, the measures of ∠8, ∠9, and ∠10 will be equal to:

∠8 = 180 - ∠7 = 180 - 37 = 143°

∠9 = 180 - ∠8 = 180 - 143 = 37°

∠10 = 180 - ∠7 = 180 - 37 = 143°

Therefore, the answers are:

∠1 = 127°

∠2 = 53°

∠3 = 127°

∠4 = 37°

∠5 = 53°

∠6 = 90°

∠7 = 37°

∠8 = 143°

∠9 = 37°

∠10 = 143°

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