Question

The angles of a triangle are (x-40),(x-30) and (2x+10) find the angles

Answer 1

$\mathfrak{\large{\underline{\underline{Answer :-}}}}$

The angles of the Triangle are 20°, 30° and 130°.

$\mathfrak{\large{\underline{\underline{Explanation :-}}}}$

Given :

The angles = (x-40),(x-30) and (2x+10)

To find :

The measure of angles

Solution :

We know that, all Angles in the triangle sum up and make 180°.

★ Equation made :

$\boxed{\tt{(x-40) + (x-30) + (2x+10) = 180^{\circ}}}$

$\tt{\implies} \: (x - 40) + (x - 30) + (2x + 10) = 180$

$\tt{\implies} \: x + x + 2x + \{- 40 + (- 30) + 10\} = 180$

$\tt{\implies} \: 4x + ( - 60) = 180$

$\tt{\implies} \: 4x = 180 + 60$

$\tt{\implies} \: 4x = 240$

$\tt{\implies} \: x = \dfrac{240}{4}$

$\tt{\implies} \: x = 60$

Value of (x - 40)

$\tt{\implies} \: 60 - 40$

$\tt{\implies} \: 20$

Value of (x - 30)

$\tt{\implies} \: 60 - 30$

$\tt{\implies} \: 30$

Value of (2x + 10)

$\tt{\implies} \: (2 \times 60) + 10$

$\tt{\implies} \: 120 + 10$

$\tt{\implies} \: 130$

The angles of the triangle are :

• 20°

• 30°

• 130°

$\therefore$ The angles of the Triangle are 20°, 30° and 130°.

$\mathfrak{\large{\underline{\underline{Verification :-}}}}$

$\tt{\implies} \: 20 + 30 + 130 \\ \tt{\implies} \: 50 + 130 \\ \tt{\implies} \: 180$

$\therefore$ The angles of the Triangle are 20°, 30° and 130°.

Answer 2

Answer :-

Given :-

The angles of triangle = (x - 40), (x - 30), (2x + 10).

To Find :-

Measure of each angle.

Solution :-

We know that the sum of angles of a triangle is equal to 180°.

So,

$\implies{\sf{(x - 40) + (x - 30) + (2x + 10) = 180 \textdegree}}$

$\implies{\sf{x - 40 + x - 30 + 2x + 10 = 180 \textdegree}}$

$\implies{\sf{4x - 60 = 180 \textdegree}}$

$\implies{\sf{4x = 180 + 60}}$

$\implies{\sf{4x = 240 \textdegree}}$

$\implies{\sf{x = \dfrac{240}{4}}}$

$\implies{\sf{x = 60}}$

So, the measure of angles are :-

$\sf{=) x - 40 = 60 - 40 = 20 \textdegree}$

$\sf{=) x - 30 = 60 - 30 = 30 \textdegree}$

$\sf{=) 2x + 10 = 120 + 10 = 130 \textdegree}$

So, the three angles are :-

$\sf{\boxed{\star{\bf{20 \textdegree, 30 \textdegree and\ 130 \textdegree}}}}$

Verification :-

$\sf{20 \textdegree + 30 \textdegree+ 130 \textdegree = 180 \textdegree}$

$\sf{180 \textdegree = 180 \textdegree}$

$\sf{Hence, Verified !!}$