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Zubin drew a circle with right triangle PRQ inscribed in it, as shown below:Q50If the measure of arc QR is 50º, what is the measure of angle PQR?

Zubin Drew A Circle With Right Triangle PRQ Inscribed In It As Shown BelowQ50If The Measure Of Arc QR Is 50º What Is The Measure Of Angle PQR class=

Sagot :

[tex]\begin{gathered} \angle PRQ=90^0(\text{ angle in a semi-circle)} \\ \angle QOR=50^0(angle\text{ subtended by the arc QR at the centre of the circle)} \\ \angle\text{QOR}=2\angle RPQ(\text{ angle at centre is twice angle at circumference)} \\ 50=2\angle RPQ \\ \angle RPQ=\frac{50}{2} \\ \angle RPQ=25^0 \end{gathered}[/tex]

Thus,

[tex]\begin{gathered} \angle RPQ+\angle PRQ+\angle PQR=180^0(sum\text{ of interior angles in triangle PQR)} \\ 25+90+\angle PQR=180^0 \\ 115+\angle PQR=180 \\ \angle PQR=180-115 \\ \angle PQR=65^0 \end{gathered}[/tex]

Hence, the measure of angle PQR is 65 degrees.

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