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, c ||d, e || f. Find the marked angle between d and f.
Solution:
Given, iron rods a, b, c, d, e and f are making a design in the bridge as shown in the figure.
Also, a ||b, c ||d, e || f
We have to find the marked angle between d and f.
Let the angle between d and e be ∠2.
Considering PQ and RS are parallel with l and m 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, ∠QPT + ∠PTU = 180°
∠QPT + ∠2 = 180°
From the figure,
∠QPT = 75°
Now, 75° + ∠PTU = 180°
∠PTU = 180° - 75°
∠2 = 105°
Let the angle between d and f be ∠3.
Similarly, ∠TUQ + ∠PTU = 180°
∠TUQ + ∠2 = 180°
Now, 105° + ∠3 = 180°
∠3 = 180° - 105°
∠3 = 75°
Therefore, the angle between d and f is 75°.
✦ Try This: In the figure given above, p∥q and r∥s. 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 90 (iii)
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, c ||d, e || f. Find the marked angle between d and f.
Summary:
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, c ||d, e || f. The marked angle between d and f is 75°.
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