In rectangle READ, find ∠EAR, ∠RAD and ∠ROD.
Solution:
Given, READ is a rectangle.
We have to find the measures of ∠EAR, ∠RAD and ∠ROD.
From the figure,
∠ROE = 60°
We know that the linear pair of angles are supplementary.
So, ∠ROE + ∠AOE = 180
60° + ∠AOE = 180°
∠AOE = 180° - 60°
∠AOE = 120°
We know that the angles opposite to the equal sides are equal.
Here, EO = DO
∠AOE = ∠ROD
So, ∠ROD = 120°
In triangle AOE,
Let ∠EAR = ∠DEA = x
By angle sum property of a triangle,
x + x + 120° = 180°
2x + 120° = 180°
2x = 60°
x = 60°/2
x = 30°
So, ∠EAR = 30°
In triangle AOD,
Let ∠RAD = ∠EDA = y
By angle sum property of a triangle,
∠RAD + ∠EAR + ∠AOD = 180°
y + y + 60° = 180°
2y = 120°
y = 120°/2
y = 60°
So, ∠RAD = ∠EDA = 60°
Therefore, the measures of the angles ∠EAR, ∠RAD and ∠ROD are 30°, 60° and 120°.
✦ Try This: In Square READ, find ∠EAR, ∠RAD and ∠ROD.
☛ Also Check: NCERT Solutions for Class 8 Maths
NCERT Exemplar Class 8 Maths Chapter 5 Problem 144
In rectangle READ, find ∠EAR, ∠RAD and ∠ROD.
Summary:
In rectangle READ, the measure of ∠EAR, ∠RAD and ∠ROD are 30°, 60° and 120°.
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