Question

The measure of two adjacent angles of a parallelogram are in the ratio 3:2. Find the measure of each of the angles of the parallelogram

Answer 1

Sum of adjacent angles of a parallelogram = 180°

Let the two unknown angles be 3x and 2x.

3x + 2x = 180°

5x = 180°

$x = \frac{180}{5}$

x = 36°.

Answer: 3x = 3×36 = 108°

2x = 2×36 =72°

Therefore, each angles are 72° , 108°, 72° , 108°.

As the angles are vertically opposite 72 degree and 72 degree, 108 degree and 108 degree.

Answer 2

$\sf\orange{ QUESTION :- }$

The measure of two adjacent angles of a parallelogram are in the ratio 3:2. Find the measure of each of the angles of the parallelogram

$\sf\orange{ ANSWER :- }$

the measures of the angles of the parallelogram are 108° , 72 ° , 108° , 72 °

$\sf\green{ STEP \: BY \: STEP \: EXPLANATION :- }$

Let ABCD be the given parallelogram

than , angle A and angle B are adjacent angles

let , angle A = (3x)° , Then B = (2x)°

angle A + angle B = 180 [ any two adjacent angle of a parallelogram are supplementary ]

→ 3x + 2x = 180

→ 5x = 180

→ x = 36°

★ angle A = ( 3 × 36 )° = 108°

★ angle B = ( 2 × 36 )° = 72°

Also ,

★ angle C = angle A = 108° [ opposite angle of a parallelogram are equal ]

★ angle D = angle B = 72 ° [ opposite angle of a parallelogram are equal ]

Hence , the measures of the angles of the parallelogram are 108° , 72 ° , 108° , 72 °