Question

calculate the value of x and the value of y.
$x = 23$ and $y = 77$
$x = 23$ and $y = 64$
$x = 33$ and $y = 74$
none of these

Explanation:

Step1: Find \(x\) using the property of supplementary angles

Supplementary angles sum to \(180^{\circ}\). So, \(x + 157^{\circ}=180^{\circ}\). Then \(x=180 - 157=23^{\circ}\).

Step2: Find \(y\) using the angle - sum property of a triangle

The sum of angles in a triangle is \(180^{\circ}\). We know \(x = 23^{\circ}\) and one angle is \(83^{\circ}\). So, \(x + y+83^{\circ}=180^{\circ}\). Substitute \(x = 23^{\circ}\) into the equation: \(23^{\circ}+y + 83^{\circ}=180^{\circ}\). Simplify the left - hand side: \(y+106^{\circ}=180^{\circ}\). Then \(y=180 - 106 = 74^{\circ}\).

Answer:

\(x = 23\) and \(y = 74\) (None of the first three options are correct, so the answer is "None of these")