Question

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

Answer 1

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°

Answer 2

Answer:

83°,97°,83°,97°

Step-by-step explanation:

Given:

Two adjacent angles = (2x+13),(3x-8)

To find:

All the angles of the parallelogram

Adjacent angles sum up to be 180° whereas the opposite angles of a parallelogram are equal

Let all the angles be a, b, c and d

So by the above statement,

(2x+13)+(3x-8)=180°

5x+5=180°

5x= 180°-5°

5x= 175°

x=175/5

x=35°

First angle = a = (2×35 + 13) = 83°

Second angle = b = (3×35 - 8) = 97°

Angle c is opposite to angle a, so

Third angle = c = 83°

Angle d is opposite to angle b, so

Fourth angle = d = 97°

So the angles are equal to 83°,97°,83°and 97°