Question

what is the value of y?
(there is a triangle ijh with a straight line through j and h. at h, the angle outside the triangle is 116 degrees. we need to find the angle y at vertex i.)
y = \boxed{\space}°

Explanation:

Step1: Find adjacent angle to 116°

The angle adjacent to \( 116^\circ \) on the straight line is supplementary, so it's \( 180^\circ - 116^\circ = 64^\circ \).

Step2: Recognize isosceles triangle

Since the triangle has two equal base angles (from the diagram's markings), both base angles are \( 64^\circ \).

Step3: Calculate \( y \) using triangle sum

The sum of angles in a triangle is \( 180^\circ \), so \( y = 180^\circ - 64^\circ - 64^\circ = 52^\circ \).

Answer:

\( 52 \)