In the diagram above, length of P S= Length of S Q and angle S Q R=112^{}. Find the value of x.

Correct Answer is : 44∘44^{}44∘

Correct Answer is : 44∘44^{}44∘

Test Index

BECE Mathematics 2010 Paper

Question : 30

Total: 40

P S=

S Q

S Q R=112^{\circ}

x

Solution:

Concept:

In an isosceles triangle, the base angles are equal.

Also, the sum of angles in a triangle is

180^\circ

Explanation:

Given

PS = SQ

, so triangle

SPQ

is isosceles.

Hence,

\angle SPQ = \angle SQP

At point

Q

\angle SQP

and

\angle SQR = 112^\circ

lie on a straight line.

So,

\angle SQP + 112^\circ = 180^\circ

Thus,

\angle SQP = 180^\circ - 112^\circ = 68^\circ

Therefore,

\angle SPQ = 68^\circ

Let

x = \angle QSP

Using the angle sum of triangle

SPQ

68^\circ + 68^\circ + x = 180^\circ

136^\circ + x = 180^\circ

x = 180^\circ - 136^\circ = 44^\circ

Answer:

x = 44^\circ

, which is option D.

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