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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.


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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 class=

Respuesta :

Dead3ill

Answer:

∠C = 62°

Step-by-step 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°

[tex]=> 3x + x + 20 = 180[/tex]

[tex]=> 4x = 180 - 20[/tex]

[tex]=> x = \frac{160}{4} = 40[/tex]

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°

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