Question

In the given figure if ab is equal to BC and Angle A equal to angle C then find the value of x

Answer 1

Given :–

• AB = BC
• ∠A = ∠C

To Find :–

• Value of x.

Solution :–

We know that,

sum of all the three angles of a triangle is 180°

In ∆BEC,

⟹ ∠EBC + ∠BEC + ∠BCE = 180° [By A.S.P.]

⟹ 55° + x + ∠BCE = 180°

⟹ x + ∠BCE = 180° – 55°

⟹ x + ∠BCE = 125°

⟹ ∠BCE = 125° – x ––––––––– (1)

Now, In ∆BDA,

⟹ ∠ABD + ∠BDA + ∠BAD = 180° [By A.S.P.]

⟹ 55° + 75° + ∠BDA = 180°

⟹ 130° + ∠BAD = 180°

⟹ ∠BAD = 180° – 130°

⟹ ∠BAD = 50°

Here,

Given that,

⟹∠BAD = ∠BCE

• ∠BCE = 50°

So,

Now, putting the equation (1),

⟹ ∠BCE = 125° – x

⟹ 50° = 125° – x

⟹ x = 125° – 50°

⟹ x = 75°

Hence,

The value of x = 75°