Question

Plz I need help with geometry homework FIND THE ANGLES

Answer 1

Answer:

1. a = 36°
2. b = 36°
3. c = 72°
4. d = 72°
5. e = 108°
6. f = 16°
7. g = 74°
8. 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°