Question

1. find the values of x and y.

(2y + 5)°
(5x - 17)° (3x - 11)°

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. Also, \((5x - 17)^{\circ}\) and \((3x-11)^{\circ}\) are supplementary to \((x + 10)^{\circ}\). First, use the linear - pair property. The sum of angles on a straight line is \(180^{\circ}\). But we can also use the vertical - angle relationship. Since \((5x - 17)\) and \((x + 10)+(3x - 11)\) are supplementary (sum to \(180^{\circ}\)), or more simply, using the vertical - angle property: \((5x-17)+(x + 10)=180\) (because \((5x - 17)\) and \((x + 10)\) are adjacent angles forming a linear pair with the angle equal to \((3x - 11)\) (vertical - angle relationship).

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Wait, no. Let's use the correct approach: \((5x-17)\) and \((3x - 11)\) are vertical angles. So \(5x-17=3x - 11\)

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Step2: Find \(y\)

We know that \((2y + 5)+(3x - 11)=90\) (because the right - angle is \(90^{\circ}\)). Substitute \(x = 3\) into the equation.

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Answer:

\(x = 3\) and \(y=43.5\)