In Fig. 5.6 AB||EF, ED||CB and ∠APE is 39°. Find ∠CQF
Solution:
Given, AB||EF and ED||CB
∠APE = 39°
We have to find the value of ∠CQF.
From the properties of angles formed by transversal on two parallel lines,
If two parallel lines are intersected by a transversal,
(i) each pair of corresponding angles is equal.
(ii) each pair of alternate interior angles is equal.
(iii) each pair of interior angles on the same side of the transversal is supplementary.
Since ED || BC intersected by a transversal AB,
The corresponding angles QBP and APE are equal.
So, ∠QBP = ∠APE
∠APE = 39°
Since AB || EF intersected by a transversal BC,
The alternate interior angles FQB and QBP are equal.
So, ∠QBP = FQB
∠FQB = 39°
We know that the linear pair of angles is always equal to 180 degrees.
So, ∠CQF + ∠FQB = 180°
∠CQF + 39° = 180°
∠CQF = 180° - 39°
Therefore, ∠CQF = 141°
✦ Try This: Out of a pair of complementary angles, one is one-third of the other. Find the angles
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 5
NCERT Exemplar Class 7 Maths Chapter 5 Sample Problem 15
In Fig. 5.6 AB||EF, ED||CB and ∠APE is 39°. Find ∠CQF
Summary:
In Fig. 5.6 AB||EF, ED||CB and ∠APE is 39°. The value of ∠CQF is 141°
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