The measure of the angles found using the properties of the interior and exterior angles of a triangle are;
2) 1 = 56°, 2 = 56°, and 3 = 74°
4) 1 = 17°, 2 = 17°
6) m∠F = 25°
9. m∠1 = 62°
10. m∠2 = 39°
11. m∠3 = 26°
12. m∠4 = 55°
13. m∠5 = 55°
14. m∠6 = 35°
The steps used to find the measure of the angles are as follows;
2) The measure of angle 1 is; 180 - (66 + 58) = 56°
∠1 ≅ ∠2, therefore, m∠2 = 56°
The measure of angle 3 is; 180 - (56 + 50) = 74°
4. The figure is an isosceles triangle, therefore;
∠1 ≅ ∠2
m∠1 = (180 - 146)/2
(180 - 146)/2 = 17
m∠1 = 17°, m∠2 = 17°
5. The external angle theorem indicates that we get;
58 = x + x
2·x = 58
x = 58°/2
x = 29
m∠F = x
m∠F = 29°
Example 3;
9. ∠1 is an interior acute angle of a right triangle, therefore;
m∠1 = 90 - 28
m∠1 = 62°
10. ∠2 is an interior acute angle of a right triangle, therefore;
m∠2 = 90 - 51
m∠2 = 39°
11. The external angle theorem indicates that we get;
m∠3 = 51 - 25
51 - 25 = 26
m∠3 = 26°
12. ∠4, and 35° are acute angles of a right triangle, therefore;
m∠4 = (90 - 35)°
(90 - 35)° = 55°
m∠4 = 55°
13. ∠5 and 35° are acute angles of a right triangle, therefore;
m∠5 = (90 - 35)°
(90 - 35)° = 55°
m∠5 = 55°
14. ∠4, and ∠6 are acute angles of a right triangle, therefore;
m∠6 = (90 - m∠4)°
(90 - m∠4)° = (90 - 55)°
(90 - 55)° = 35°
m∠6 = 35°