In Fig. 6.8, PB = PD. The value of x is
a. 85°
b. 90°
c. 25°
d. 35°
Solution:
Given, the figure represents a triangle ABC.
Also, PB = PD
We have to find the value of x.
Linear pairs of angles are formed when two lines intersect each other at a single point.
Linear pair angles are supplementary angles as their sum is 180°.
Considering triangle PBD,
∠1 + 120° = 180°
∠1 = 180° - 120°
∠1 = 60°
Since PB = PD, ∠1 = ∠2 = 60°
Similarly, ∠2 + ∠3 = 180°
60° + ∠3 = 180°
∠3 = 180° - 60°
∠3 = 120°
Considering triangle PDC,
By angle sum property of a triangle,
We know that the sum of all the three interior angles of the triangle is equal to 180 degrees.
35° + ∠3 + x = 180°
35° + 120° + x = 180°
x = 180° - 35° - 120°
x = 60° - 35°
Therefore, x = 25°
✦ Try This: The sides of a triangle are 3 cm, 4 cm and 3 cm. Determine the type of triangle
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 6
NCERT Exemplar Class 7 Maths Chapter 6 Problem 8
In Fig. 6.8, PB = PD. The value of x is: a. 85°, b. 90°, c. 25°, d. 35°
Summary:
In Fig. 6.8, PB = PD. The value of x is 25°
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