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°