A road crosses a railway line at an angle of 30° as shown in Fig.5.45. Find the values of a, b and c
Solution:
Given, a road crosses a railway line at an angle of 30°.
We have to find the value of a, b and c.
Considering l and m are parallel and P is a transversal,
If two parallel lines are intersected by a transversal, each pair of corresponding angles is equal.
So, x = y
From the figure,
x = 30°
Now, y = 30°
We know that the sum of a linear pair of angles is always equal to 180 degrees.
Now, c + y = 180°
c + 30° = 180°
c = 180° - 30°
c = 150°
Similarly, c + ∠1 = 180°
150° + ∠1 = 180°
∠1 = 180° - 150°
∠1 = 30°
If two parallel lines are intersected by a transversal, each pair of corresponding angles is equal.
So, ∠1 = a
Now, a = 30°
We know that the sum of a linear pair of angles is always equal to 180 degrees.
So, a + ∠2 = 180°
30° + ∠2 = 180°
∠2 = 180° - 30°
∠2 = 150°
If two parallel lines are intersected by a transversal, each pair of alternate interior angles is equal.
∠2 = b
So, b = 150°
Therefore, the values of a, b and c are 30°, 150° and 150°.
✦ Try This: Write all the linear pairs of angles.
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 5
NCERT Exemplar Class 7 Maths Chapter 5 Problem 88
A road crosses a railway line at an angle of 30° as shown in Fig.5.45. Find the values of a, b and c
Summary:
A road crosses a railway line at an angle of 30° as shown in Fig.5.45. The values of a, b and c are 30°, 150° and 150°
☛ Related Questions:
- The legs of a stool make an angle of 35° with the floor as shown in Fig. 5.46. Find the angles x and . . . .
- Iron rods a, b, c, d, e and f are making a design in a bridge as shown in Fig. 5.47, in which a ||b, . . . .
- Iron rods a, b, c, d, e and f are making a design in a bridge as shown in Fig. 5.47, in which a ||b, . . . .