Line HJ bisects angle IHL, Line HK bisects angleJHL, and m<IHK is 51 degrees. Find m<IHL
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To find the measure of angle IHL, we can use the Angle Bisector Theorem. According to the theorem, when a line bisects an angle, it divides the angle into two congruent angles.
Since line HJ bisects angle IHL, angle IHL is divided into two congruent angles, angle IHJ and angle JHL. Similarly, line HK bisects angle JHL, so angle JHL is divided into two congruent angles, angle JHK and angle KHL.
We are given that angle IHK measures 51 degrees. Since angle IHJ and angle JHK are congruent, each must measure 51 degrees as well.
Since angle JHK and angle KHL are congruent, each must also measure 51 degrees.
Therefore, angle JHL is the sum of angle IHJ, angle JHK, and angle KHL, which is:
m<JHL = m<IHJ + m<JHK + m<KHL = 51 degrees + 51 degrees + 51 degrees = 153 degrees.
Since angle IHL is divided into angle IHJ and angle JHL, we can find the measure of angle IHL by subtracting angle JHL from the straight angle, which measures 180 degrees:
m<IHL = 180 degrees - m<JHL = 180 degrees - 153 degrees = 27 degrees.
Therefore, the measure of angle IHL is 27 degrees.