Question

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

Answer 1

Explanation:

$\sf \large \red{\underline{ Question:-}}$

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

$\\\\\sf \large \red{\underline{Given:-}}$

The measures of two adjacent angles of a parallelogram are in the ratio 3:2.

$\\\\\sf \large \red{\underline{To \: Find:-}}$

Find the measure of each of the angles of the parallelogram.

$\\\\\sf \large \red{\underline{Solution :- }}$

$\text{ \sf suppose the angles be equal to 3x and 2x.}$

$\boxed{ \sf \orange{ we \: have \: ardjacent \: angles \: of \: a \: parallelogram \: = 180}}$

$\\ \sf \underline{ \green{putting \: all \: values : }}$

$\: \\ \sf \to \: 3x + 2 x = 180\: \\ \\ \sf \to \: \: \: \: \: \: \: \: \: \: \:5x = 180 \\ \\ \: \sf \to \: \: \: \: \: \: \: \: \: \: \:x \: = \frac{180}{5} \\ \\ \sf \to \: \: \: \: \: \: \: \: \: \: \:x \: = \cancel{ \frac{180}{5} } \\ \\ \sf \to \: \: \: \: \: \: \: \: \: \: \purple{x = 36}$

$\sf \to \: 3x \\ \sf \to \: 3 \times 36 \\ \sf \to \red{108 }\\ \\ \\ \sf \to \: 2x \\ \sf \to \: 2 \times 36 \\ \sf \to \orange{72}$

$\sf \large\underline{ \blue{verification }} \huge \dag$

$\\ \\ \sf \to 3x + 2x = 180 \\ \\ \sf \to \: 3 \times 36 +2 \times 36 = 180 \\ \\ \sf \to \: 108 + 72 = 180 \\ \\ \sf \to \:180 = 180 \\ \\ \large \underline{ \pink{ \sf \: hence \: verified}} \huge \dag$

Answer 2

Answer:

∠A = 108°

∠B = 72°

∠C = 108°

∠D = 72°

Step-by-step explanation:

Let,

The angles of the parallelogram :

∠A = 3x

∠D = 2x

We know that,

Adjacent angles of a parallelogram are supplementary

⇒ ∠A + ∠D  = 180°

⇒ 3x + 2x = 180°

⇒ 5x  = 180°

⇒ x = 180° / 5

⇒ x = 36°

Value of 3x :

⇒ 3 (36)

⇒ 108°

Value of 2x :

⇒ 2 (36)

⇒ 72°

Opposite angles are equal in the parallelogram

So,

⇒ ∠A = ∠C = 108°

⇒ ∠D = ∠B = 72°

∴ ∠A = 108°

∠B = 72°

∠C = 108°

∠D = 72°