Amisha makes a star with the help of line segments a, b, c, d, e and f, in which a || d, b || e and c || f. Chhaya marks an angle as 120° as shown in Fig. 5.48 and asks Amisha to find the ∠x, ∠y and ∠z. Help Amisha in finding the angles.
Solution:
Given, Amisha makes a star with the help of line segments a, b, c, d, e and f.
Also, a || d, b || e and c || f.
Chhaya marks an angle as 120°.
We have to find the angles x, y and z.
Vertically opposite angles are angles that are opposite one another at a specific vertex and are created by two straight intersecting lines.
Vertically opposite angles are equal to each other.
From the figure,
∠a = 120°
If two parallel lines are intersected by a transversal, each pair of interior angles on the same side of the transversal is supplementary.
So, ∠x + ∠a = 180°
∠x + 120° = 180°
∠x = 180° - 120°
∠x = 60°
If two parallel lines are intersected by a transversal, each pair of alternate interior angles is equal.
So, ∠x = ∠1
Now, ∠1 = 60°
We know that the sum of a linear pair of angles is always equal to 180 degrees.
So, ∠1 + ∠y = 180°
60° + ∠y = 180°
∠y = 180° - 60°
∠y = 120°
If two parallel lines are intersected by a transversal, each pair of interior angles on the same side of the transversal is supplementary.
So, ∠z + ∠a = 180°
∠z + 120° = 180°
∠z = 180° - 120°
∠z = 60°
Therefore, the values of the angles x, y and z are 60°, 120° and 60°.
✦ Try This: In the figure given above, l∥m. Find the values of x,y and z.
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 5
NCERT Exemplar Class 7 Maths Chapter 5 Problem 91
Amisha makes a star with the help of line segments a, b, c, d, e and f, in which a || d, b || e and c || f. Chhaya marks an angle as 120° as shown in Fig. 5.48 and asks Amisha to find the ∠x, ∠y and ∠z. Help Amisha in finding the angles.
Summary:
Amisha makes a star with the help of line segments a, b, c, d, e and f, in which a || d, b || e and c || f. Chhaya marks an angle as 120° as shown in Fig. 5.48 and asks Amisha to find the ∠x, ∠y and ∠z. The values of the angles x, y and z are 60°, 120° and 60°.
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