Question

Two adjacent angle of parallelogram are (2x+13) and (3x-8). The value of x is​

Answer 1

Answer:

∠C = ∠A = 88°

∠D = ∠B = 97°

Step-by-step explanation:

Given:

Two adjacent angle of a parallogram are (2x+13) and (3x-8).

To find out:

Find all the angles of parallelogram?

Solution:

Let ABCD is a parallelogram and the two adjacent angles A and B are 2x + 13 and 3x - 8 respectively.

∠A = 2x + 13

∠B = 3x - 8

Since, ∠A and ∠B are a pair of adjacent interior angles and AD II BC .

Therefore,

∠A + ∠B = 180°

➪ ( 2x + 13 ) + ( 3x - 8 ) = 180°

➪ 5x + 5 = 180°

➪ 5x = 180 - 5

➪ 5x = 175

➪ x = 175/5

➪ x = 35°

∠A = 2x + 13 = 2 × 35° + 18° = 70° + 18° = 88°

∠B = 3x - 8 = 3 × 35° - 8° = 105° - 8° = 97°

Since Opposite angles of parallelogram are equal ,

∠C = ∠A = 88°

∠D = ∠B = 97°