Three lines AB, CD and EF intersect each other at O. If ∠AOE = 30° and ∠DOB = 40° (Fig. 5.51), find ∠COF.
Solution:
Given, three lines AB, CD and EF intersect each other at O.
Also, ∠AOE = 30° and ∠DOB = 40°
We have to find the measure of ∠COF.
We know that the sum of all angles lying on a straight line is equal to 180 degrees.
∠AOE + ∠EOD + ∠BOD = 180°
From the figure,
30° + ∠EOD + 40° = 180°
70° + ∠EOD = 180°
∠EOD = 180° - 70°
∠EOD = 110°
We have to find the angles x, y and z.
Vertically opposite angles are angles that are opposite one another at a specific vertex and are created by two straight intersecting lines.
Vertically opposite angles are equal to each other.
From the figure,
∠EOD = ∠COF
Therefore, ∠COF = 110°
✦ Try This: In the figure given above, l∥m. Find the values of x.
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 5
NCERT Exemplar Class 7 Maths Chapter 5 Problem 94
Three lines AB, CD and EF intersect each other at O. If ∠AOE = 30° and ∠DOB = 40° (Fig. 5.51), find ∠COF.
Summary:
Three lines AB, CD and EF intersect each other at O. If ∠AOE = 30° and ∠DOB = 40° (Fig. 5.51), then ∠COF is 110°.
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