Question

triangle hij with vertex h, i, j. angle at h is ( x^circ ), angle at i is ( 2x^circ ), angle at j is ( 81^circ ) (vertical angle with ( 81^circ ) below j, horizontal line jk to the right of j, vertical line below j with ( 81^circ ) angle).

Explanation:

Step1: Identify vertical angles

Vertical angles are equal, so the angle at \( J \) in triangle \( HIJ \) is \( 81^\circ \) (since it's vertical to the \( 81^\circ \) angle shown).

Step2: Use triangle angle sum

The sum of angles in a triangle is \( 180^\circ \). So, \( x + 2x + 81 = 180 \).

Step3: Solve for \( x \)

Combine like terms: \( 3x + 81 = 180 \). Subtract 81 from both sides: \( 3x = 180 - 81 = 99 \). Divide by 3: \( x = \frac{99}{3} = 33 \).

Answer:

\( x = 33 \)