Question

IMMEDIATE HELP NEEDED!!!! 50 POINTS

​Quadrilateral ABCD​ is inscribed in this circle.



What is the measure of angle C?

Enter your answer in the box.


°

Answer 1

∠C = 62°

Explanation:

GIVEN :-

• Cyclic quadrilateral ABCD
• ∠A = (2x + 38)°
• ∠D = (x + 20)°
• ∠B = (3x)°

TO FIND :-

• The measure of ∠C

FACTS TO KNOW BEFORE SOLVING :-

• A cyclic quadrilateral is a quadrilateral inscribed in a circle.
• In a cyclic quadrilateral , sum of the opposite interior angles is equal to 180°

PROCEDURE :-

As ABCD is a cyclic quadrilateral ,

∠B + ∠D = 180°

`=> 3x + x + 20 = 180`

`=> 4x = 180 - 20`

`=> x = (160)/(4) = 40`

Putting the values of x gives :-

∠A = (2×40 + 38)° = 118°

∠B = (3×40)° = 120°

∠D = (40 + 20)° = 60°

Also,

∠A + ∠C = 180°

⇒ ∠C = 180° - 118° = 62°