Question

IN A PARALLELOGRAM ABCD; ANGLE A IS 3 TIMES THE MEASURE OF ANGLE B FIND ALL ANGLES

Answer 1

let angle B be x
angle A = 3x
anglw C = 3x
angle D = x
3x+3x+x+x=360
8x=360
×=45

Answer 2

The measure of ∠A, ∠B, ∠C and ∠D are 135°, 45°, 135° and 45° respectively.

Step-by-step explanation:

We have drawn the parallelogram for your reference.

Let the measure of Angle B be 'x'.

According to question, Angle A is 3 times the measure of Angle B.

So, the measure of Angle A be '3x'.

Since ABCD is a parallelogram, so the measure of opposite angle is equal and consecutive angles are supplementary.

$\therefore\angle A+\angle B=180\°$

On putting the values, we get;

$3x+x=180\°\\\\4x=180\°\\\\x=\frac{180}{4}=45\°$

$\therefore\angle B=x=45\°$

$\angle A=3x=3\times45=135\°$

$\angle A =\angle C=135\°\\\\And\angle B =\angle D=45\°$

Hence The measure of ∠A, ∠B, ∠C and ∠D are 135°, 45°, 135° and 45° respectively.