Question

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, and

d. The interior angle a is labeled as left parenthesis x plus 15 right parenthesis degrees. The angle b is labeled as left parenthesis x plus 10 right parenthesis degrees. The angle d is labeled as left parenthesis x plus 24 right parenthesis degrees

Answer 1

Answer:

∠c = 92°

Step-by-step explanation:

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, and  d

The interior angle a = (x+15)° degrees. The angle b = (x + 10)° parenthesis d = (x + 24)°

∠a + ∠b + ∠c + ∠d = 360°

=> (x +15)° + (x + 10)°  + ∠c + (x + 24)° = 360°

=> ∠c = (311 -3x)°

as Quadrilateral abcd is inscribed in this circle

so ∠a + ∠c = 180°

=> (x +15)° + (311 -3x)° = 180°

=> 326° - 2x°  = 180°

=> 2x° = 146°

=> x° = 73°

∠c = (311 -3x)°

=> ∠c = (311 -3(73)°

=>  ∠c = (311 -219)°

=> ∠c = 92°