Question

Two adjacent angles of a parallelogram are in the ratio 2:3. Find the measures of all
the angles
​

Answer 1

Step-by-step explanation:

Two adjacent angles of a parallelogram are in the ratio 2:3.

2x°+3x°=180°..(Adjacent angles

is supplementary)

5x°=180°

x=180°/5°

x=36

2x°=(2×36)°

=72°

3x°=(3×36)°

=108°

The measures of all angles of parallelogram is 72°,108°,72°,108°.

Answer 2

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Given :-

• Two adjacent angles of a parallelogram are in the ratio 2:3

To find :-

• Measure of all angles of the parallelogram.

Solution :-

Let x be the common multiple of the ratio 2 : 3

Let the four angles of the parallelogram be :-

• $\angle$ CDA
• $\angle$ DAB
• $\angle$ ABC
• $\angle$ BCD

Let $\angle$ DAB = 2x

Let $\angle$ ABC = 3x

Let these two angels be adjacent angles of the parallelogram.

As we know :

• Sum of adjacent angles of a parallelogram are supplementary.

=> $\angle$ DAB +  $\angle$ ABC = 180

=> 2x + 3x = 180

=> 5x = 180

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

=> x = 36

Value of x is 36

Put this value of x in the value of ratio of angles.

$\angle$ DAB : 2x = 2 × 36 = 72°

$\angle$ ABC : 3x = 3 × 36 = 108°

$\angle$ CDA = $\angle$ ABC = 108° $\rm\underbrace{Opposite\:angles\:are\:congruent}$

•°• $\angle$ CDA = 108°

$\angle$ DAB = $\angle$ BCD = 72° $\rm\underbrace{Opposite\:angles\:are\:congruent}$

•°•$\angle$ BCD = 72°