Question

In quadrilateral PQRS, if ∠P = 60° and ∠Q : ∠R : ∠S = 2:3:7, then find the measure of∠S.

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Given:

∠P = 60°

∠Q : ∠R : ∠S = 2:3:7

To find:

The measure of ∠S

Solution:

The measure of ∠S is 175°.

We can find the angle by following the given steps-

We know that the sum of all the angles of a quadrilateral equals 360°.

In PQRS, the sum of all angles=360°

Angle P+angle Q+angle R+angle S=360°

We know that ∠Q: ∠R: ∠S = 2:3:7 and ∠P = 60°.

Let the angles Q, R, and S be 2x, 3x, and 7x, respectively.

Now we will use the values to determine the angles.

60°+2x+3x+7x=360°

2x+3x+7x=360°-60°

12x=300°

x=300°/12

x=25°

We can find the measure of angle S by substituting the value of x.

Angle S=7x=7×25°

=175°

Therefore, the measure of ∠S is 175°.