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Find the values of the variables in the parallelogram. The diagram is not drawn to scale. (Image is attached below)thank you in advance :)

Find the values of the variables in the parallelogram. The diagram is not drawn to-example-1
User Monzoor Tamal
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1 Answer

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For this problem, we are given a parallelogram with a diagonal drawn, inside it there are markings for a few angles. We need to determine the unknown angles.

Opposite sides of a parallelogram are parallel, this means we can treat the diagonal as a transversal line that crosses two parallel lines. Since this is the case, the angles 33º and xº are alternate interior angles and have the same length:


x=33º

The opposite angles in a parallelogram are congruent, therefore:


z=109º

The sum of internal angles is 360º, therefore we have:


\begin{gathered} 2\cdot109+2\cdot(x+y)=360\\ \\ 218+66+2y=360\\ \\ 284+2y=360\\ \\ 2y=360-284\\ \\ 2y=76\\ \\ y=38 \end{gathered}

The value of x is 33º, the value of y is 38º and the value of z is 109º.

User Brian Leathem
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