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