In the given figure, find angle QSR.
please help answer with explanation required!!!
Answers
Answer:
50° is the answer.
angle QOR=100°
angle QSR=1/2 angle QOR
THUS , QSR=50°
The measure of angle QSR is 65°.
Given:
Angle QPR=50°
To find:
Angle QSR
Solution:
The lines PQ and PR are the circle's tangents and thus, perpendicular to the radius.
So, angle OQP=angle ORP=90°
Now, in quadrilateral OQPR,
angle OQP+angle ORP+angle QPR+angle QOR=360°
Using values,
90°+90°+50°+angle QOR=360°
230°+angle QOR=360°
angle QOR=360°-230°
angle QOR=130°
Now, the angles minor QOR and major QOR=360°.
So, the major angle QOR=360°-130°=230°.
We know that the angle QTR is at the circumference and thus, its measure is half of the major angle QOR.
Angle QTR=Major angle QOR/2=230°/2=115°
In the cyclic quadrilateral QTRS, angle QTR+ angle QSR=180°.
Using values,
115°+angle QSR=180°
Angle QSR=180°-115°
Angle QSR=65°
Therefore, the measure of angle QSR is 65°.