27.8k views
0 votes
Quadrilateral ABCD ​ is inscribed in this circle.

What is the measure of angle C?

Enter your answer in the box.


°

Quadrilateral ABCD ​ is inscribed in this circle. What is the measure of angle C? Enter-example-1
User Jerica
by
8.7k points

2 Answers

5 votes

Answer:

107

explanation:

I took the quiz

User Ketan Ghumatkar
by
7.7k points
1 vote
By the Inscribed Quadrilateral Theorem, a quadrilateral can only be inscribed if and only if opposite angles are supplementary. This means that
\angle D \text{ and } \angle B are supplementary, or add up to 180°. This gives us the equation
(3x + 9)° + (2x - 4)° = 180°
Combine like terms:
5x + 5 = 180
Subtract 5 from each side:
5x + 5 - 5 = 180 - 5
5x = 175
Divide both sides by 5:
5x/5 = 175/5
x = 35
This means that
m \angle D=3(35)+9=114 \\m \angle B=2(35)-4 = 66 \\m \angle A=2(35) + 3=73
We take these 3 angles away from 360 and we will have the measure of angle C:
360 - 114 - 66 - 73 = 107°
User Jose Vega
by
8.0k points

No related questions found