Question

calculate the value of x and the value of y. options: x = 38 and y = 48; x = 20 and y = 38; x = 20 and y = 48; none of these. there is a triangle with an exterior angle of 160° (related to angle x°) and an interior angle of 112° (angle at another vertex, angle y°).

Explanation:

Step1: Find the value of \( x \)

We know that a straight angle is \( 180^{\circ} \). The angle adjacent to \( 160^{\circ} \) (which is \( x^{\circ} \)) forms a straight line, so we use the equation \( x + 160 = 180 \).
Solving for \( x \), we subtract \( 160 \) from both sides: \( x = 180 - 160 = 20 \).

Step2: Find the value of \( y \)

The sum of the interior angles of a triangle is \( 180^{\circ} \). In the triangle, we know one angle is \( 112^{\circ} \) and another angle is \( x = 20^{\circ} \). Let the third angle be \( y \). So we use the equation \( 112 + x + y = 180 \).
Substitute \( x = 20 \) into the equation: \( 112 + 20 + y = 180 \).
Simplify the left - hand side: \( 132 + y = 180 \).
Subtract \( 132 \) from both sides: \( y = 180 - 132 = 48 \).

Answer:

\( x = 20 \) and \( y = 48 \) (The option: \( x = 20 \) and \( y = 48 \))