Answer:
m∠1 = 35°
m∠2 = 65°
m∠3 = 29°
m∠4 = 115°
m∠5 = 65°
m∠6 = 36°
m∠7 = 144°
Explanation:
∠4 is vertically opposite the angle with 115° measure. Vertically opposite angles are equal
So m∠4 = 115°
∠2 and ∠4 are on a straight line. So are ∠4 and ∠5
The sum of angles on a line must equal 180°
So m∠2 = m∠5 = 180 - 115 = 65°
∠1, 80° and ∠2 are the interior angles of a triangle. So their sum must be 180°
m∠1 + 80 + 65 = 180
m∠1 = 180 - 80 - 65 = 180 - 145 = 35°
m∠3 + 61° + 90° = 180°
So m∠3 = 180 - 61 - 90 = 29°
m∠5 + 61° + m∠7 + 90° = 360° since they are the four angles of a 4 sided polygon
65 + 61 + 90 + m∠7 = 360
m∠7 = 360 - 65 - 61 - 90 = 360 - 216 = 144°
∠6 and ∠7 lie on a straight line - sum of these angles = 180
m∠6 + m∠7 = 180
m∠6 + 144 = 180
m∠6 = 180 - 144 =36°
m∠3 + m∠4 + m∠6 = 180 since they are the interior angles of a triangle.
m∠3 + 115 + 36 = 180
m∠3 = 180 - 115 - 36 = 280 - 151 = 29°