mahiai247
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  • 04-03-2020
  • Mathematics
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Quadrilateral ABCD ​ is inscribed in this circle.



What is the measure of ∠A ?

Enter your answer in the box.

Quadrilateral ABCD is inscribed in this circle What is the measure of A Enter your answer in the box class=

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shilpa85475 shilpa85475
  • 12-03-2020

The measure of ∠A is 137°.

Solution:

Given data:

Angle A = 43°

A quadrilateral inscribed in a circle is called cyclic quadrilateral.

∠A and ∠C are opposite angles in a cyclic quadrilateral.

In cyclic quadrilateral, opposite angles are supplementary.

⇒ m∠A + m∠C = 180°

⇒ 43° + m∠A = 180°

Subtract 43° from both sides of the equation, we get

⇒ m∠A = 137°

Hence the measure of ∠A is 137°.

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