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Maths-

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Question

In the figure above, $Error converting from MathML to accessible text.$ and $Error converting from MathML to accessible text.$ are parallel, $Error converting from MathML to accessible text.$ and $Error converting from MathML to accessible text.$ are parallel, CD = CE, and the measure of $Error converting from MathML to accessible text.$ is 115⁰. What is the measure of $Error converting from MathML to accessible text.$ ?

85^∘
115^∘
125^∘
140^∘

The correct answer is: 115^∘

HINT: From the information given in the question, find the angles.
Complete step by step solution:
Given BC and AD are parallel and AB and EC are parallel.
From this, we can conclude that ABCE is a parallelogram.
$straight angle ABC space equals space 115 to the power of ring operator$ (given)
So, $straight angle AEC space equals space straight angle ABC space equals space 115 to the power of ring operator$ (Since opposite angles of a parallelogram are equal.)
And $straight angle BCE space equals space 65 to the power of ring operator$ (Since consecutive angles of a parallelogram are supplementary angles to each other.)
We get that,
$straight angle DEC space equals space 65 to the power of ring operator$ (Since BC ∥ AD and CE acts as a transversal, so $straight angle BCE$ and $straight angle DEC$ are alternate interior angles.)
Since CD = CE, ΔECD is an isosceles triangle.
So we get, $straight angle DEC space equals space straight angle EDC space equals space 65 to the power of ring operator$ (Since two angles opposite to the equal sides of an isosceles triangle are equal.)
Hence, $straight angle ECD space equals space 180 space minus open parentheses 65 space plus space 65 right parenthesis space equals space 50 to the power of ring operator close$ .(Since the sum of all angles of a triangle is 180°.)
To find, $straight angle BCD space equals space straight angle ECD space plus space straight angle ECB space equals space 50 to the power of ring operator plus space 65 to the power of ring operator space equals space 115 to the power of ring operator$
So, $straight angle BCD space equals space 115 to the power of ring operator$
Hence option B is the answer.

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