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°
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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