In Fig 5.58, PQ, RS and UT are parallel lines. If c = 57° and a = 3/c , find the value of d
Solution:
Given, PQ, RS and UT are parallel lines.
c = 570 and a = 3/c
We need to find the value of d.
Considering PQ || UT with PT as transversal,
If two parallel lines are intersected by a transversal, each pair of alternate interior angles are equal.
So, ∠QPT = ∠UTP
So, a + b = c
c/3 + b = c
b = c - c/3
b = 3c - c/3
b = 2(57°)/3
b = 38°
Considering PQ || RS with PR as transversal,
If two parallel lines are intersected by a transversal, each pair of interior angles on the same side of the transversal is supplementary.
So, ∠QPR + ∠PRS = 180°
b + d = 180°
d = 180° - b
d = 180° - 38°
d = 142°
Therefore, the value of d = 142°
✦ Try This: In the figure, two parallel lines l and m are cut by two transversal p and q. Find the values of y.
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 5
NCERT Exemplar Class 7 Maths Chapter 5 Problem 105 (i)
In Fig 5.58, PQ, RS and UT are parallel lines. If c = 57° and a = 3/c , find the value of d
Summary:
PQ, RS and UT are parallel lines. If c = 57° and a = 3/c,the value of d = 142°
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