Question

for each part below, use the figure to fill in the blank. if necessary, you may learn what the markings on a figure indicate. (a) find m ∠k. (b) find hi. m ∠k = \square ° hi = \square

Explanation:

Part (a)

Step1: Identify Triangle Type

Triangle \( KJL \) has \( LK = KJ = 13 \), so it's isosceles with \( \angle L = \angle J = 35^\circ \).

Step2: Sum of Angles in Triangle

Sum of angles in a triangle is \( 180^\circ \). Let \( m\angle K = x \). Then \( x + 35^\circ + 35^\circ = 180^\circ \).

Step3: Solve for \( x \)

\( x = 180^\circ - 35^\circ - 35^\circ = 110^\circ \).

Step1: Identify Triangle Type

Triangle \( HIG \) has \( \angle I = \angle G \), so it's isosceles with \( HI = HG \)? Wait, no, wait: Wait, the equal angles are at \( I \) and \( G \), so the sides opposite are \( HG \) and \( HI \)? Wait, no, angle at \( I \) and \( G \) are equal, so sides opposite: side opposite \( \angle I \) is \( HG \), side opposite \( \angle G \) is \( HI \). Wait, no, in triangle \( HIG \), angles at \( I \) and \( G \) are equal, so sides opposite them ( \( HG \) and \( HI \) )? Wait, no, angle at \( I \): opposite side is \( HG \); angle at \( G \): opposite side is \( HI \). Wait, but the side given is \( HG = 9 \)? Wait, no, the side \( HG \) is 9? Wait, the figure shows \( HG = 9 \), and angles at \( I \) and \( G \) are equal, so triangle is isosceles with \( HI = HG \)? Wait, no, wait: angle at \( I \) and \( G \) are equal, so sides opposite are equal. So side opposite \( \angle I \) is \( HG \), side opposite \( \angle G \) is \( HI \). Therefore, \( HI = HG = 9 \).

Step2: Conclude Length

Thus, \( HI = 9 \).

Answer:

\( 110 \)

Part (b)