In the diagram, A B is parallel to D E, angle A B C=81^{} and angle D C E=20^{}. Use the information to answer the question below: Find the value of y.

Correct Answer is : 79∘79^{}79∘

Correct Answer is : 79∘79^{}79∘

Test Index

BECE Mathematics 2022 Paper

Question : 19

Total: 40

A B

D E

A B C=81^{\circ}

D C E=20^{\circ}

y

Solution:

Concept:

Use alternate interior angles of parallel lines and the angle sum of a triangle.

Explanation:

Since

AB \parallel DE

, the transversal gives

\angle ABC = \angle CDE

as alternate angles.

Given

\angle ABC = 81^\circ

, so

\angle CDE = 81^\circ

\triangle CDE

\angle DCE = 20^\circ

and

\angle CDE = 81^\circ

Using the angle sum of a triangle:

\angle DEC = 180^\circ - 81^\circ - 20^\circ

\angle DEC = 79^\circ

Again, because

AB \parallel DE

\angle BAC = \angle DEC

as alternate angles.

Therefore,

y = \angle BAC = 79^\circ

Answer:

y = 79^\circ

, which is option C.

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