Question

8. The adjacent angles of a parallelogram are (x + 25) and (2x + 35)'. Find the
measure of all angles of parallelogram.​

Answer 1

Answer:

65,115 ,65,115

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Answer 2

Answer:

The measure of all angles of a parallelogram are 65°, 115°, 65° and 115° respectively.

Step-by-step explanation:

Given:

• The adjacent angles of a parallelogram are (x + 25)° and (2x + 35)°.

To find:

• The measure of all angles of parallelogram.

Solution:

We know that adjacent angles of a parallelogram are supplementary, i.e, they add up to 180°.

• (x + 25) + (2x + 35) = 180°
• x + 25 + 2x + 35 = 180°
• 3x + 60 = 180
• 3x = 180 - 60
• 3x = 120
• x = 120/3
• x = 40°

Then,

• First angle = 40° + 25°
• First angle = 65°

• Second angle = 2 × 40° + 35°
• Second angle = 80° + 35°
• Second angle = 115°

Opposite angles of parallelogram are equal, so we know that other two angles i.e, third and fourth angle are 65° and 115° respectively.

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