In the given figure find the value of x ?
Thank you!

EXPLANATION:

In ∆ ABC, ∠CAB = 65°

AB = AC

⇛∠ACB =∠CBA

Since the angles opposite to equal sides are equal.

Let ∠ACB = ∠CBA = A°

We know that

The sum of all angles in a triangle is 180°

⇛∠ACB + ∠CBA + ∠CAB = 180°

⇛A°+A°+65° = 180°

⇛2A°+65° = 180°

⇛2A° = 180°-65°

⇛2A° = 115°

⇛A° = 115°:2 =115°/2

⇛A° = 57.5°

∠ACB =∠CBA =57.5°

and

In ∆ BCD , ∠BCD = 110°

and

BC = CD

⇛∠BDC =∠CBD

Since the angles opposite to equal sides are equal.

Let ∠BDC =∠CBD = M°

The sum of all angles in a triangle is 180°

∠BCD+∠BDC + ∠CBD = 180°

⇛M°+M°+110° = 180°

⇛2M°+110°° = 180°

⇛2M° = 180°-110°

⇛2M° = 70°

⇛M° = 70° :2 =70°/2

⇛M° = 35°

.°. ∠BDC = ∠CBD = 35°

Now,

∠B = ∠ABC+ ∠CBD

⇛x = 57.5°+35°

⇛x = 92.5°

.°. x = 92.5°

Answer: The value of x is 92.5°.

Additional comment: •The sum of all angles in a triangle is 180°

• the angles opposite to equal sides are equal. •The exterior angle of a triangle formed by extending one side is equal to the sum of the opposite interior angles.

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not only in mathematics, scientific proof also are required in the other field of science. also maths proofs are of particular structure, containing steps and logics. so proving is like doing science, it is science. that's why it is important to prove. 

an inaccurate proof leads to errors, or stating results that are not accurate.  which wil mess the probelm up you dont want this