Question

two adjacent angles of a parallelogram are (5x+65) degrees and (85-2x)degrees find the measure of each angle of a parallrlogram

Answer 1

We know that opposite angles of parallelograms are equal
And its sum of all the sides = 180
(5x + 65)+(85-2x)=180
5x-2x+65+85=180
3x+150=180
3x=180-150=30
3x=30
X=30/3=10
1st adjacent side = 5x+65=5*10+65=50+65=115
2nd adjacent side = 85-2x=85-2*10=85-20=65
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Answer 2

Given:

Two adjacent angles of a parallelogram are (5x+65)° and (85-2x)°

To Find:

The measure of each angle of a parallelogram.

Solution:

We know that,

opposite angles of a parallelogram are equal

sum of adjacent angles = 180°

So,

(5x + 65)° + (85-2x)° = 180°

5x - 2x + 65° + 85° = 180°

3x + 150° = 180°

3x = (180-150)° = 30°

3x = 30°

x = (30/3)° = 10°

Putting the value of x = 10° in the equations, we get

1st adjacent side = 5x + 65 = 5*10 + 65 = 50 + 65 = 115°

2nd adjacent side = 85 - 2x = 85 - 2*10 = 85 - 20 = 65°

Hence, measure of each angle of the parallelogram is 115°, 65°, 115° and 65°.