CTET 2 Math and Science 2011 Paper

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Question : 46 of 120

Marks: +1, -0

In the given figure, PS = SQ = SR and ∠SPQ = 54°. Findthe measure of < x.

54°
72°
108°
36°

Solution:

In ΔRSQ

SQ = SR

∴∠{SQR}=∠{QRS}

⇒{x}=∠{QRS}

Now, in ΔPSQ,

∴∠PS=∠SQ

54^{∘}=∠{SQP}

Now, in Δ PQR,

∠{P}+∠{PQR}+∠{R}=180^{∘}

54^{∘}+54^{∘}+x^{∘}+x^{∘}=180^{∘}

⇒2{x}^{∘}=72^{∘}

⇒x°=36°

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