In a quadrilateral PQRS, If the sum of measure of angles $$\angle{Q}$$ and $$\angle{S}$$ is $$150^o$$ while the measure of angles $$\angle{P}$$ and $$\angle{R}$$ are in ratio 4 : 3, then the measure of $$\angle{R}$$ will be​

Correct option is B

Given:

In quadrilateral PQRS, sum of angles ∠Q and ∠S is 150°.

∠P and ∠R are in the ratio 4 : 3.

To Find:

Measure of ∠R.

Solution:

Step 1: Use the sum of angles of a quadrilateral

The sum of all interior angles of a quadrilateral is always 360°.

∠P + ∠Q + ∠R + ∠S = 360°

Substitute the given sum of ∠Q and ∠S

From the question, ∠Q + ∠S = 150°. Substituting this into the equation:

∠P + ∠R + 150° = 360°

Simplify:

∠P + ∠R = 210°

Use the ratio of ∠P and ∠R

The angles ∠P and ∠R are in the ratio 4 : 3. Let:

∠P = 4x and ∠R = 3x

Substitute into ∠P + ∠R = 210°:

4x + 3x = 210°

Combine terms:

7x = 210°

Solve for x:

x = 210 ÷ 7 = 30°

Find ∠R

Now, ∠R = 3x. Substitute x = 30°:

∠R = 3 × 30° = 90°

The measure of ∠R is 90°.