Question

In the figure given above, ABCD is a straight line. Find x
(a) 25°
(b) 35°
(C) 45°
(d) 55°​

Answer 1

Answer:

(a) 25°

Explanation:

It's shown in the figure that In the ∆ECD

ED = CD, So ∆ECD is an isosceles triangle.

Let ∠CED = a

∠CED = ∠ECD ( isosceles triangle)

Now, ECD is a triangle, so

⟹ ∠CED + ∠EDC + ∠DCE = 180°

⟹ a + 50° + a = 180°

⟹ 2a + 50° = 180°

⟹ 2a = 180° - 50°

⟹ 2a = 130°

⟹ a = 130°/2

⟹ a = 65°

So, ∠CED = ∠ECD = 65°

Given that ABCD is a line, So

⟹ ∠BCE + ∠ECD = 180°

⟹ ∠BCE + 65° = 180°

⟹ ∠BCE = 180° - 65°

⟹ ∠BCE = 115°

In the figure, we can see, ∠ABF and ∠EBC are vertically opposite angles. So,

⟹ ∠ABF = ∠EBC

⟹ 40° = ∠EBC

EBC is a triangle, so

⟹ ∠EBC + ∠BCE + ∠CEB = 180°

⟹ 40° + 115° + x = 180°

⟹ 155° + x = 180°

⟹ x = 25°

Measure of x is 25°