Question

f the angles of a triangle are (x-35⁰), (x-25⁰) and (x/2-10⁰), then find x.​

Answer 1

GIVEN :-

• Angles of the triangle are (x-35) , (x-25) and (x/2 - 10) .

TO FIND :-

• Value of x.

TO KNOW :-

• Angle Sum Property :- Sum of all interior angles of the triangle is 180°.

SOLUTION :-

According to Angle Sum Property, sum of (x-35) , (x-25) and (x/2 - 10) is 180°.

$\\ \implies \sf \: (x - 35) + (x - 25) + \left( \dfrac{x}{2} - 10\right)= 180 \\ \\ \implies \sf \: x - 35 + x - 25 + \dfrac{x}{2} - 10 = 180 \\ \\ \implies\sf \: 2x + \dfrac{x}{2} \: - 70 = 180 \\ \\ \implies\sf \: \dfrac{2(2x) + x}{2} = 180 + 70 \\ \\ \implies \sf \: \dfrac{4x + x}{2} = 250 \\ \\ \sf \: \implies5x = 500 \\ \\ \implies\sf \: x = \cancel \dfrac{500}{5} \\ \\ \implies \underline{ \boxed{ \red{\sf \: x = 100}}}$

Hence , value of x is 100.

Angles are :-

• x - 35 = 65°
• x - 25 = 75°
• x/2 - 10 = 40°