Question

Two adjacent angles of a parallelogram are (2x+25)°and(3x−5)°. Find the value of xand hence find the measure of each of its angles

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

Value of x = 32

Angle P = 89°

Angle Q = 91°

Angle R = 89°

Angle S = 91°

Step-by-step explanation:

Given:

• Two adjacent angles of a parallelogram (2x + 25)° and (3x - 5)°

To Find:

• The value of x
• Each angle of the parallelogram

Solution:

Let us assume the angles of the parallelogram are P, Q, R and S

Hence,

Angle P = (2x + 25)°

Angle Q = (3x - 5)°

We know that in a parallelogram adjacent angles are supplementary.

That is,

Angle P + Angle Q = 180

Hence,

2x + 25 + 3x - 5 = 180

5x + 20 = 180

5x = 180 - 20

5x = 160

x = 200/5

x = 32

Hence the value of x is 32.

Now we have to find the angles of the parallelogram

Angle P = 2x + 25

Angle P = 2 × 32 + 25

Angle P = 64 + 25

Angle P = 89°

Angle Q = 3x - 5

Angle Q = 3 × 32 - 5

Angle Q = 96 - 5

Angle Q = 91°

We know that in a parallelogram opposite angles are equal.

Angle P = Angle R

Angle Q = Angle S

Hence,

Angle R = 89°

Angle S = 91°

Verification:

We know that in a quadrilateral sum of all angles is equal to 360°.

Hence,

Angle P + Angle Q + Angle R + Angle S = 360

89 + 91 + 89 + 91 = 360

180 + 180 = 360

360 = 360

Hence verified.