In the diagram, O is the center of the circle. {PQ} and {RS} are tangents to the circle. Find the value of (M + N).

Correct Answer is : 90∘^{}∘

Correct Answer is : 90∘^{}∘

Test Index

WAEC Mathematics 2020 Paper

Question : 40

Total: 48

\overline{PQ}

\overline{RS}

Solution:

Concept:

A tangent to a circle is perpendicular to the radius drawn to the point of contact, forming a

90^{\circ}

angle.

Explanation:

In the given triangle,

m

and

n

are two angles, and the third angle is the right angle formed by the radius and the tangent.

So, the three angles of the triangle are

m

n

, and

90^{\circ}

Using the sum of angles in a triangle:

m + n + 90^{\circ} = 180^{\circ}

m + n = 180^{\circ} - 90^{\circ}

m + n = 90^{\circ}

Answer:

90^{\circ}

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