Question

10 The adjacent angles in a parallelogram
are (3x + 10) and (x + 20). Find the
measures of the four angles.​

Answer 1

✬ Question ✬

The adjacent angles in a parallelogram  are (3x + 10)° and (x + 20)°. Find the  measures of the four angles.​

✬ Given ✬

The adjacent angles in a parallelogram  are (3x + 10)° and (x + 20)°.

✬ To find ✬

The  measures of the four angles.​

✬ Solution ✬

As we know that the sum of the adjacent angles of a parallelogram is 180°, we can say-

(3x + 10) + (x + 20) = 180

⇒ 4x + 30 = 180

⇒ 4x = 180 - 30

⇒ 4x =  150

⇒ x = 150/4

⇒ x = 37.5

✬ Hence ✬

x = 37.5

(3x + 10)° = 122.5°

(x + 20)° = 57.5°

Since the opposite angles are equal, the remaining two angles are  112.5° and 57.5°.

✬ Therefore ✬

The angles are 122.5°, 57.5°, 122.5° and 57.5°.

Hope this helps you.