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Maths-

General

Easy

Question

In the figure, $P Q perpendicular P S comma P Q vertical line vertical line S R comma straight angle S Q R equals 28 to the power of ring operator text and end text straight angle Q R T equals 65 to the power of ring operator text , end text$ then find the value of x and y.

hint Hint:

Hint :-Find the ∠QSR as the exterior angle is ∠QRT is given
We get angle x = ∠QSR they both are alternate interior angles
We find the value of y by using the sum of angles in triangle PSQ is 180 °.
Ans :- x =37° and y = 53°

The correct answer is: x =37° and y = 53°

Explanation :-
Step 1:-Find ∠QSR
We know that in a triangle, the exterior angle is always equal to the sum of the interior opposite angles.
∠QSR +∠SQR = ∠QRT
∠QSR +28° = 65°
∠QSR = 65° -28° = 37°
Step 2:- Find value of x
PQ || SR and QS intersects both the lines
We get angle x = ∠QSR ( alternate interior angles)
x =37°
Step 3:- Find value of y
In PSQ, ∠P + x + y = 180 °(sum of angles in triangles)
90°+37° +y =180 °
y = 180-127
y = 53 °

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