Question

Quadrilateral ABCD ​ is inscribed in this circle. What is the measure of angle A? Enter your answer in the box. ° A quadrilateral inscribed in a circle. The vertices of the 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 x minus 36 right parenthesis degrees. The angle B is labeled as 28 degrees. The angle D is labeled as x degrees.

Answer 1

Answer:

m∠A = 116°

Step-by-step explanation:

For better understanding of the solution, see the attached figure of the problem :

The quadrilateral ABCD is inscribed in a circle, Thus the quadrilateral ABCD is a cyclic quadrilateral.

Also, Sum of opposite angles of a cyclic quadrilateral is supplementary.

Now, m∠A = (x - 36)°, m∠B = 28° and m∠D = x°

But, since the sum of opposite angles is 180°

⇒ 28° + x° = 180°

⇒ x = 180 - 28

⇒ x = 152

So, m∠A = (x - 36)°

⇒ m∠A = (152 - 36)°

⇒ m∠A = 116°

Answer 2

Answer:

116°

Step-by-step explanation:

A quadrilateral inscribed in a circle

so opposite angles will have sum = 180°

∠B + ∠D = 180°

∠B = 28°

∠D = x°

28° + x° = 180°

=> x° = 152°

∠A = (x - 36)°

∠A = x° - 36°

∠A = 152° - 36°

∠A = 116°