The measure of angle O in the given parallelogram is equal to 105°.
As given in the question,
Given parallelogram LMNO,
As shown in the attached diagram we have,
Measure of angle L = ( x + 40 )°
Measure of angle O = (3x)°
In the parallelogram LMNO,
LM is parallel to NO .
LO is the transversal.
∠MLO and ∠NOL are interior angles and are supplementary.
m ∠MLO + m ∠NOL = 180°
⇒ ( x + 40 )° + ( 3x )° = 180°
⇒ 4x° = 180° - 40°
⇒x = 140° / 4
⇒ x = 35°
Measure of ∠O = 3x°
= 3(35°)
= 105°
Therefore, the measure of ∠O in the parallelogram LMNO with the given conditions is equal to 105°.
The complete question is :
What is the measure of angle O in parallelogram LMNO?
Diagram of parallelogram LMNO is attached.
m∠O = ?
a. 35° b. 75° c. 105° d. 155°
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