Hushar Mulga
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In a cyclic ▢ABCD, twice the measure of ∠A is thrice the measure of ∠C. Find the measure of ∠C? 36° 72° 90° 108°

Chapter 3 – Circle – Text Book Solution

Problem Set 3 | Q 1.08 | Page 83

Four alternative answers for the following question is given. Choose the correct alternative

In a cyclic ▢ABCD, twice the measure of ∠A is thrice the measure of ∠C. Find the measure of ∠C?

  • 36°
  • 72°
  • 90°
  • 108°
solution

ABCD is a cyclic quadrilateral.

2∠A = 3∠C        .....(1) (Given)

Now,

∠A + ∠C = 180º     ......(Opposite angles of a cyclic

quadrilateral are supplementary)

⇒`3/2` ∠C + ∠C = 180º    [From (1)]

​⇒ `5/2`∠C = 180º

⇒ ∠C = `(2 xx 180º)/5` = 72º

Thus, the measure of ∠C is 72º.

Hence, the correct answer is 72º.

Explanation:- To find the measure of angle C in the cyclic quadrilateral ABCD, we are given that 2 times angle A is equal to 3 times angle C. We also know that opposite angles in a cyclic quadrilateral add up to 180 degrees. Therefore, we can write the following equations:

angle A + angle C = 180 degrees …(1) 2 * angle A = 3 * angle C …(2)

From equation (2), we can write angle A in terms of angle C as:

angle A = (3/2) * angle C

Substituting this in equation (1), we get:

(3/2) * angle C + angle C = 180 degrees

Simplifying this equation, we get:

(5/2) * angle C = 180 degrees

Solving for angle C, we get:

angle C = (2 * 180 degrees) / 5 = 72 degrees

Therefore, the measure of angle C is 72 degrees.

Chapter 3 – Circle – Text Book Solution

Problem Set 3 | Q 1.08 | Page 83

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