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°.
