Question

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

Answer 1

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Answer 2

Step-by-step explanation:

Given :-

The adjacent angles of a parallelogram are

(x + 25)° and (2x + 35)°.

To find :-

Find the measure of all angles of parallelogram?

Solution :-

Given that :

The adjacent angles of a parallelogram are

(x + 25)° and (2x + 35)°.

We know that

The adjacent angles in a Parallelogram are Supplementary.

=> (x + 25)° + (2x + 35)° = 180°

=> (x+2x) +(25°+35°) = 180°

=> 3x + 60° = 180°

=> 3x = 180°-60°

=> 3x = 120°

=> x = 120°/3

=>x = 40°

Now,

If x = 40° then (x+25)°

= 40°+25°

= 65°

If x = 40° then (2x+35)°

= 2×40°+35°

= 80°+35°

= 115°

The adjacent angles are 65° and 115°

We know that

In a Parallelogram opposite angles are equal.

So ,

Opposite angle of 65° = 115°

Opposite angle of 115° = 65°

The angles are 65° ,115°, 65° and 115°

Answer:-

The measures of all angles in the given Parallelogram are 65° ,115°, 65° and 115°

Used formulae:-

• The adjacent angles in a Parallelogram are Supplementary.

• In a Parallelogram opposite angles are equal.