Question

Please find the value of x​

Answer 1

Step-by-step explanation:

Solution :-

Method-1:-

In ∆ ABC , angle A = x°

angle B = a+a = 2a

angle C = b+b = 2b

We know that

The sum of the three angles in a triangle is 180°

=> <A + < B + <C = 180°

=> x°+2a+2b = 180°

=> 2a+2b = 180°-x°

=> 2(a+b) = 180°-x°

=> a+b = (180°-x°)/2 -------------(1)

and

In ∆ BOC,

angle BOC = 130°

angle CBO = a°

angle BCO = b°

We know that

The sum of the three angles in a triangle is 180°

=> <BOC + < CBO+ <BCO = 180°

=> 130°+a+b = 180°

=> a+b = 180°-130°

=> a+b = 50° --------------(2)

From (1)&(2)

=> (180°-x°)/2 = 50°

=> 180°-x° = 50°×2

=> 180°-x° = 100°

=> x = 180°-100°

=> x = 80°

Therefore, x = 80°

Method-2:-

We know that

In ∆ ABC, the angle bisectors of B and C meet at O then < BOC = 90°+(<BAC )/2

We have ,

< BOC = 130°

< BAC = x°

=> 130° = 90°+(x°)/2

=> 130° -90° = x°/2

=> 40° = x°/2

=> x° = 40°×2

=> x° = 80°

Answer:-

The measurement of x for the given problem is 80°

Used formulae:-

→ The sum of the three angles in a triangle is 180°

→In ∆ ABC, the angle bisectors of B and C meet at O then < BOC = 90°+(<BAC )/2