Question

If the adjacent angle of a parallelogram are (2x-5)° and (3x+10)° find the angles of a parallelogram​

Answer 1

To Find :-

• The angles of parallelogram.

Solution:

Given that,

The adjacent angles of parallelogram are :-

• (2x-5)°
• (3x+10)°

We know that,

Sum of adjacent angles of parallelogram = 180°

Therefore,

• (2x-5)° + (3x+10)° = 180°

By simplifying,

⟹ (2x-5) + (3x+10) = 180

⟹ 2x - 5 + 3x + 10 = 180

⟹ 2x + 3x = 180 - 10 + 5

⟹ 5x = 180 - 10 + 5

⟹ 5x = 170 + 5

⟹ 5x = 175

⟹ x = 175/5

⟹ x = 35

∴ The adjacent angles are :-

• (2x-5)° = (2*35-5)° = (70-5)° = 65°
• (3x+10) = (3*35+10)° = (105+10) = 115°

Hence, The adjacent angles of parallelogram are 65° and 115°.

Required Answer :-

• The adjacent angles of parallelogram are 65° and 115°.

Answer 2

Answer :-

• Adjacent angles of the parallelogram = 65° and 115°

Step by step explanation :-

Given :-

1. The given figure is a parallelogram.
2. Measure of adjacent angles = (2x-5)° and (3x+10)°

To find :-

• Measure of angles in the parallelogram.

Concept :-

• Application of properties of a parallelogram.

• Suitable simplification of the equation for finding the angles of the parallelogram.

Solution :-

Given that, (2x+5)° and (3x+10)° are the adjacent angles of the parallelogram.

As we know that,

☆ Sum of the adjacent angles of a parallelogram is supplimentary.

It means the sum of adjacent angles is 180°.

According to question :-

⠀⠀⠀⠀⠀⠀⠀⠀⠀(2x-5)° + (3x+10)° = 180°

⠀⠀⠀⠀⠀⠀⠀⠀⠀2x-5+3x+10 = 180

⠀⠀⠀⠀⠀⠀⠀⠀⠀5x+5 = 180°⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀5x = 180°-5°

⠀⠀⠀⠀⠀⠀⠀⠀⠀5x = 175°

⠀⠀⠀⠀⠀⠀⠀⠀⠀x = (175/5)°

⠀⠀⠀⠀⠀⠀⠀⠀⠀x = 35°

First adjacent angle :-

☆ (2x-5)°

⇒ [2(35)-5]

⇒ 70°-5°

⇒ 65°

Second adjacent angle :-

☆ (3x+10)°

⇒ [3(35)+10]

⇒ 105°+10°

⇒ 115°

Hence,

• Angles of the parallelogram = 65°,115°,65° and 115°.