Question

Measures of two adjacent angles of parallelogram are equal .Find the measures of all angles of the parallelogramare in the ratio 3:2 find the angles of parallelogram

Answer 1

Let the angles be 3x , 2x , 3x , 2x

Sum of all the angles of parallelogram = 360

3x + 2x + 3x + 2x = 360

10x = 360

x = 36

3x = 3 * 36 = 108

2x = 2 * 36 = 72

Answer 2

$\huge\star{\underline{\mathtt{\red{A}\pink{N}\green{S}\blue{W}\purple{E}\orange{R}}}}$

$\huge{\red{\ddot{\smile}}}{\huge{\pink{\ddot\smile}}}{\huge{\purple{\ddot{\smile}}}}{\huge{\orange{\ddot{\smile}}}}{\huge{\blue{\ddot{\smile}}}}$

Let the measures of two adjacent angles, ∠A and ∠B, of parallelogram ABCD are in the ratio of 3:2.

Let ∠A = 3x and ∠B = 2x

We know that the sum of the measures of adjacent angles is 180º for a parallelogram.

∠A + ∠B = 180º

3x + 2x = 180º

5x = 180º

∠A = ∠C = 3x = 108º (Opposite angles)

∠B = ∠D = 2x = 72º (Opposite angles)

Thus, the measures of the angles of the parallelogram are 108º, 72º, 108º, and 72º.