In parallelogram MODE, the bisector of ∠M and ∠O meet at Q, find the measure of ∠MQO.
Solution:
Given, MODE is a parallelogram.
The bisector of ∠M and ∠O meet at Q.
We have to find the measure of ∠MQO.
We know that the adjacent angles of a parallelogram are supplementary.
So, ∠EMO + ∠DOM = 180°
Dividing by 2 on both sides, we get
1/2 ∠EMO + 1/2 ∠DOM = 90°
From the figure,
∠QMO + ∠QOM = 90° ------------------------- (1)
In triangle MOQ,
By angle sum property of a triangle,
∠QOM + ∠QMO + ∠MQO = 180°
From (1),
90° + ∠MQO = 180°
∠MQO = 180° - 90°
Therefore, ∠MQO = 90°
✦ Try This: ABCD is a rhombus with each side of length 20 cm. Angle ABC and ADC measure 60° each. Find the length of the diagonal AC.
☛ Also Check: NCERT Solutions for Class 8 Maths
NCERT Exemplar Class 8 Maths Chapter 5 Problem 155
In parallelogram MODE, the bisector of ∠M and ∠O meet at Q, find the measure of ∠MQO.
Summary:
In parallelogram MODE, the bisector of ∠M and ∠O meet at Q, the measure of ∠MQO is 90 degrees.
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