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BECE Mathematics 2017 Paper

Question : 15

Total: 40

x

Solution:

Angle ABD = Angle BDE (Alternate Angles)

Since the sides

|B D|

and

|B E|

are equal (Base angles of isosceles triangle are the same), Angle

B D E=

Angle BED

Angles on a straight line sum up to

180^{\circ}

\; ABD+2x+56=180

\; ABD=180-56-2x

\; ABD=124-2x

But

A B D=B D E

and

B D E=B E D

ABD=BDE=BED=124-2x

But angles in a triangle sum up to

180^{\circ}

\;2x+124-2x+124-2x=180

\;2x-2x-2x+124+124=180

\;-2x+248=180

\;248-180=2x

\;68=2x

Divide both sides by 2

\;\frac{68}{2}=\frac{2x}{2}

\;34=x

\;x=34

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