Answered

Get the answers you need from a community of experts on IDNLearn.com. Get the information you need from our experts, who provide reliable and detailed answers to all your questions.

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°

We value your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Your questions deserve reliable answers. Thanks for visiting IDNLearn.com, and see you again soon for more helpful information.