Question

□ABCD is cyclic. If ∠A =(7y - 21) ° and ∠C = (4y+3)° . Find measure of ∠A.

Answer 1

Answer :-

101degree

Answer 2

Given:

∠A =(7y - 21)°

∠C = (4y+3)°

To find:

The measure of angle A

Solution:

The measure of angle A is 105°.

We can find the angle by following the given steps-

We know that ABCD is cyclic.

So, the angles at opposite ends will be supplementary.

Here angle A and angle C are opposite to each other.

The sum of angle A and angle C is equal to 180°.

Angle A+Angle C=180°

Angle A=(7y-21)° and Angle C=(4y+3)°.

Substituting the values of angle A and C, we get

(7y-21)+(4y+3)=180°

7y-21+4y+3=180

11y-18=180

11y=180+18

11y=198

y=198/11

y=18°

Now, to find the measure of angle A, we can put the value of y.

Angle A=7y-21

On putting y=18°, we get

Angle A=7×18-21

=126-21

Angle A=105°

Therefore, the measure of angle A is 105°.