In Fig. 5.7, CD intersects the line AB at F, ∠CFB = 50° and ∠EFA = ∠AFD. Find the measure of ∠EFC
Solution:
Given, CD intersects the line AB at F.
Measure of the angle CFB is 50 degrees.
∠EFA = ∠AFD.
We have to find the measure of the angle EFC.
Since CD intersects AB at F,
The vertically opposite angles are ∠AFD and ∠CFB.
Vertically opposite angles theorem states that two opposite vertical angles formed when two lines intersect each other are always equal (congruent) to each other.
∠AFD = ∠CFB
So, ∠AFD = 50°
Given, ∠EFA = ∠AFD
So, ∠EFA = 50°
We know that the linear pair of angles is always equal to 180 degrees.
∠CFB + ∠EFA + ∠EFC = 180°
50° + 50° + ∠EFC = 180°
100° + ∠EFC = 180°
∠EFC = 180° - 100°
Therefore, ∠EFC = 80°
✦ Try This: From the given figure, find the consecutive interior angles.
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 5
NCERT Exemplar Class 7 Maths Chapter 5 Sample Problem 17
In Fig. 5.7, CD intersects the line AB at F, ∠CFB = 50° and ∠EFA = ∠AFD. Find the measure of ∠EFC
Summary:
In Fig. 5.7, CD intersects the line AB at F, ∠CFB = 50° and ∠EFA = ∠AFD. The measure of ∠EFC is 80 degrees
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