Math  /  Geometry

QuestionIn the parallelogram, mKLO=78m \angle K L O=78 and mMLO=42m \angle M L O=42. Find mKJMm \angle K J M. The diagram is not to scale.
Select one: a. 110 b. 120 c. 78 d. 60

Studdy Solution

STEP 1

1. In a parallelogram, opposite angles are equal.
2. The sum of angles around a point is 360360^\circ.
3. The diagonals of a parallelogram bisect each other.

STEP 2

1. Determine the relationship between the given angles and the angles in the parallelogram.
2. Calculate the measure of KJM \angle KJM .

STEP 3

Identify the relationship between the given angles and the angles in the parallelogram. Since KLO=78 \angle KLO = 78^\circ and MLO=42 \angle MLO = 42^\circ , we know that these angles are part of the angles around point O O .

STEP 4

Calculate the measure of KJM \angle KJM . Since KLO \angle KLO and MLO \angle MLO are angles around point O O , and diagonals bisect each other, we have:
KLO+MLO+KJM+JMO=360 \angle KLO + \angle MLO + \angle KJM + \angle JMO = 360^\circ

STEP 5

Substitute the known values into the equation:
78+42+KJM+JMO=360 78^\circ + 42^\circ + \angle KJM + \angle JMO = 360^\circ

STEP 6

Calculate the sum of KLO \angle KLO and MLO \angle MLO :
78+42=120 78^\circ + 42^\circ = 120^\circ

STEP 7

Subtract the sum from 360 360^\circ to find the sum of KJM \angle KJM and JMO \angle JMO :
360120=240 360^\circ - 120^\circ = 240^\circ

STEP 8

Since diagonals bisect each other, KJM=JMO \angle KJM = \angle JMO . Therefore, each angle is half of 240 240^\circ :
KJM=2402=120 \angle KJM = \frac{240^\circ}{2} = 120^\circ
The measure of KJM \angle KJM is:
120 \boxed{120^\circ}

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