The angles of each letter are as follows:
∠a = 124°
∠b = 56°
∠c = 56°
∠d = 38°
∠e = 38°
∠f = 76°
∠g = 66°
∠h = 104°
∠k = 76°
∠n = 86°
∠p = 38°
∠a = 180 - 56 = 124°(total angle on a straight line)
∠b = 56°(vertically opposite angles)
∠c = 56°(corresponding angle to ∠b) Note this is possible because there are 2 parallel lines and a transversal.
2∠d + ∠d + 66 = 180 (sum of angles in a triangle)
3∠d = 180 - 66
3∠d = 114
∠d = 114 / 3
∠d = 38°
∠d = ∠e (given)
Therefore,
∠e = 38°
∠d + 66 + ∠f = 180
38 + 66 + ∠f = 180
∠f = 76°
Recall external angle of a triangle is equals to the sum of the opposite angles. Therefore,
∠f + ∠g = ∠d + ∠h
∠f + ∠g = 38 + 104
76 + ∠g = 142
∠g = 66°
∠d is one of the base angles of an isosceles triangle. Therefore base angles of the isosceles triangle are equal. This means the other base angle opposite ∠d in the isosceles triangle is congruent to ∠d.
Therefore,
2∠d + ∠h = 180(sum of angles in a triangle)
76 + ∠h = 180
∠h = 180 - 76
∠h = 104°
∠h + ∠k = 180 (sum of angles on a straight line)
∠k = 76°
∠n = 180 - ∠d - ∠c (angles on a straight line)
∠n = 86°
∠p = 180 - 56 - ∠n (sum of angle in a triangle)
∠p = 38°
Therefore, the angles of the letters are:
∠a = 124°
∠b = 56°
∠c = 56°
∠d = 38°
∠e = 38°
∠f = 76°
∠g = 66°
∠h = 104°
∠k = 76°
∠n = 86°
∠p = 38°
read more: brainly.com/question/18178458?referrer=searchResults
