Answer:
- w = 105°
- x = 30°
- y = z = 75°
Explanation:
You want to know the measures of the marked angles in the given figure.
Parallel lines
The two lines are indicated as parallel, so alternate interior angles are congruent:
x ≅ 30°
y ≅ z
Isosceles triangle
Angle z is a base angle of the isosceles triangle with vertex angle 30°. Consequently, its measure is ...
z = (180° -30°)/2 = 75°
Linear pair
The angles z and w are a linear pair, so supplementary:
w = 180° -z = 180° -75° = 105°
The measures of the angles are ...
- w = 105°
- x = 30°
- y = z = 75°
__
Additional comment
The relation for z comes from the fact that the sum of angles in a triangle is 180°, and the two base angles of an isosceles triangle have the same measure:
2z +30° = 180°
2z = 180° -30°
z = (180° -30°)/2
<95141404393>