Question

find the value of each variable in the figure on the right.
x = 82 (simplify your answer.)
y = (simplify your answer.)

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. In the given triangle, we have two known angles 29° and 69°. Let the third - interior angle be \(z\). So, \(z+29^{\circ}+69^{\circ}=180^{\circ}\).

Step2: Calculate the third - interior angle \(z\)

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Since \(x\) and \(z\) are vertical angles, \(x = 82^{\circ}\) (vertical angles are equal).

Step3: Use the linear - pair property

\(x\) and \(y\) form a linear pair. A linear pair of angles is supplementary, i.e., \(x + y=180^{\circ}\).

Step4: Solve for \(y\)

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Answer:

98