Answer:
- a = 36°
- b = 36°
- c = 72°
- d = 72°
- e = 108°
- f = 16°
- g = 74°
- h = 70°
Step-by-step explanation:
You are expected to know and make use of the following relations:
- vertical angles are congruent
- angles of a linear pair are supplementary
- angles of a triangle sum to 180°
- alternate interior angles are congruent (at parallel lines)
- corresponding angles are congruent (at parallel lines)
- acute angles of a right triangle are complementary
- base angles of an isosceles triangle are congruent
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For this problem, it isn't always easiest to work the questions in order. It is best to start with the angles easiest to find from those given.
b and 144° are a linear pair, so b = 180° -144° = 36°
a and b are alternate interior angles, so a = b = 36°
2d and 144° are corresponding angles, so d = 144°/2 = 72°
e is the apex angle of an isosceles triangle with base angles 36°, so is 180° -2(36°) = 108° = e
f and 164° are a linear pair, so f = 180° -164° = 16°
g and f are complementary, so g = 90° -16° = 74°
g+h is a vertical angle with 144°, so is congruent to that. h = 144° -74° = 70°
c is the base angle of an isosceles triangle with b as the vertex angle. That means c = (180° -36°)/2 = 72°
