Question

Geometry help plssss

Answer 1

Given:

ABCD is a quadrilateral inscribed in a circle.

m∠A = (2x + 38)°, m∠B = 3x° and m∠D = (x + 20)°

To find:

Measure of angle C

Solution:

In cylic quadrilateral, sum of the measures of opposite angles are 180°.

m∠B + m∠D = 180°

3x° + x° + 20° = 180°

4x° + 20° = 180°

Subtract 20° from both sides.

4x° + 20° - 20° = 180° - 20°

4x° = 160°

Divide by 4 on both sides, we get

x° = 40°

In cylic quadrilateral, sum of the measures of opposite angles are 180°.

m∠A + m∠C = 180°

2x° + 38° + m∠C = 180°

2(40)° + 38° + m∠C = 180°

80° + 38° + m∠C = 180°

118° + m∠C = 180°

Subtract 118° from both sides, we get

m∠C = 62°

The measure of angle C is 62°.

Answer 2

Answer:

62°

Step-by-step explanation:

Opposite angles supplement

(x + 20) + 3x = 180

4x = 160

x = 40

Angle A: 2(40) + 38 = 118

Angle C: 180 - 118 = 62