Answered

​Quadrilateral ABCD​ is inscribed in this circle. What is the measure of angle C? Enter your answer in the box. ° A quadrilateral inscribed in a circle. The vertices of quadrilateral lie on the edge of the circle and are labeled as A, B, C, D. The interior angle A is labeled as left parenthesis 2 x plus 38 right parenthesis degrees. The angle B is labeled as 3 x degrees. The angle D is labeled as left parenthesis x plus 20 right parenthesis degrees.



Answer :

semsee45

Answer:

m∠C = 62°

Step-by-step explanation:

A cyclic quadrilateral is a four-sided polygon where all its vertices lie on the circumference of a single circle.

The opposite angles in a cyclic quadrilateral sum to 180°. In quadrilateral ABCD, angles B and D are opposite angles. Therefore, we can set the sum of their angle expressions equal to 180° and solve for x:

m∠B + m∠D = 180°

3x° + (x + 20)° = 180°

3x + x + 20 = 180

4x + 20 = 180

4x = 160

x = 40

To find the measure of angle C, set the sum of the expressions for opposite angles A and C equal to 180°, substitute x = 40, and solve for angle C:

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°

m∠C = 180° - 118°

m∠C = 62°

Therefore, the measure of angle C is 62°.

View image semsee45

Other Questions