In Fig. 5.3, four line segments PQ, QR, RS and ST are making the letter W, PQ||RS and QR||ST. If the angle between PQ and QR is 39°, find the values of x and y
Solution:
Given, four line segments PQ, QR, RS and ST make the letter W.
PQ || RS and QR || ST
The angle between PQ and QR is 39 degrees.
We have to find the values of x and y.
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 PQ || RS intersected by transversal QR
The alternate interior angles are x° and 39°
So, x = 39°
Since QR || ST intersected by transversal RS,
The alternate interior angles are y° and x°
So, y = x
y = 39°
Therefore, the values of x and y are 39° and 39°.
✦ Try This: In Fig., PQ+RS, ∠AEF = 95°, ∠BHS = 110° and ∠ABC = x°. Then the value of x is,
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 5
NCERT Exemplar Class 7 Maths Chapter 5 Sample Problem 12
In Fig. 5.3, four line segments PQ, QR, RS and ST are making the letter W, PQ||RS and QR||ST. If the angle between PQ and QR is 39°, find the values of x and y
Summary:
In Fig. 5.3, four line segments PQ, QR, RS and ST are making the letter W, PQ||RS and QR||ST. If the angle between PQ and QR is 39°, the values of x and y are 39° and 39°
☛ Related Questions:
- In Fig. 5.4, are the angles 1 and 2 of the letter N forming a pair of adjacent angles? Give reasons
- In Fig. 5.5, the points A, O and B are collinear. Ray OC ⊥ ray OD. Check whether ∠AOD and ∠BOC are c . . . .
- In Fig. 5.5, the points A, O and B are collinear. Ray OC ⊥ ray OD. Check whether ∠AOC and ∠BOC are s . . . .