Find the value of x in Fig. 6.38.
Solution:
Given, ABC is a triangle.
We have to find the value of x.
Exterior angles are defined as the angles formed between the side of the polygon and the extended adjacent side of the polygon.
The exterior angle is ∠ACD = ∠ACE + ∠ECD.
From the figure,
∠ACD = ∠x + 90°
The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two opposite interior angles of the triangle.
By exterior angle property,
∠ACD = ∠A + ∠B
∠x + 90° = 80° + 30°
∠x + 90° = 110°
∠x = 110° - 90°
∠x = 20°
Therefore, the value of x is 20°
✦ Try This: In ∆XYZ, if ∠X = ∠Z, and exterior angle XYA = 110°, then find the angles of the triangle.
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 6
NCERT Exemplar Class 7 Maths Chapter 6 Problem 126
Find the value of x in Fig. 6.38.
Summary:
The value of x in Fig. 6.38 is 20°.
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