Answer:
m<JMK = 54
m<JKH = 63
m<HLK = 90
m<HJL = 27
m<LHK = 63
m<JLK = 27
Step-by-step explanation:
1. Solve for m<JMK
It is given that (<HMJ) and (<JMK) form line (HK), meaning that they are supplementary angles. Thus, their degree measures add up to (180), using this one can form the following equation,
(<HMJ) + (<JMK) = 180
126 + (<JMK) = 180
(<JMK) = 54
2. Solve for m<JKH
It is given that the figure is a rectangle, one of the properties of a rectangle is that diagonals are congruent, and the diagonals bisect each other. This means that segments (JM) and (MK) are congruent. Hence, the triangle (JMK) is an isoceles triangle. Therefore, one can use the base-angles theorem, which states that (<MJK) is congruent to (<JKH). Since the sum of angle measures in any triangle is (180), one can form the following equation,
(<JMK) + (<MJK) + (<JKH) = 180
54 + 2(<JKH) = 180
<JKH = 63
3. Solve for m<HLK
As per its definition, the corner angles in a rectangle are always (90) degrees, this property is applicable for the given rectangle. Thus, (<HLK) = 90 degrees.
4. Solve for m<HJL
To solve for this angle, one can use similar logic as they did to solve for (<JKH). Form the following equation and solve,
(<HMJ) + (<HJL) + (<JHK) = 180
126 + 2(<HJL) = 180
(<HJL) = 27
5. Solve for m<LHK
The vertical angles theorem states that when two lines intersect, the opposite angles are congruent. One can apply this theorem here and say (<JMK) = (<HML). Then, to solve for this angle, one can use the same logic that they used to solve for (<JKH) and (<HJL). Form the equation and solve,
(<HML) +(<LHK) + (<HLJ) = 180
54 + 2(<LHK) = 180
<LHK = 63
6.Solve for m<JLK
To solve for this angle, one can use the same logic that they used to solve for (<LHK). Form the equation and solve,
(<LMK) + (<JLK) + (HKL) = 180
126 + 2(<JLK) = 180
<JLK = 27