34. The measures of the angles of a triangle are (2x + 5)º. (4x + 10)

1.	34. The measures of the angles of a triangle are (2x + 5)º. (4x + 10)° and(3x - 15). What type of triangle is it?(1) Scalene right angled triangle(2) Scalene obtuse angled triangle(3) Right angled isosceles triangle(4) Acute angled isosceles triangle
Answer» Answer : Right angled isosceles triangle. Solution : Given : (2x + 5)º, (4x + 10)° and (3x - 15)° are angles of a triangle. To Find : Type of triangle. Let's solve , We know that , SUM of all angles of a triangle = 180° So, (2x + 5)º + (4x + 10)° + (3x - 15)° = 180° ➩ 2x + 5 + 4x + 10 + 3x - 15 = 180° $\implies \sf 9x + \cancel{15}\: \: \cancel{-15}$ = 180° $\implies \sf <klux>X</klux> = \dfrac{180}{9} \\ \\ \implies \sf \red \boxed{\sf{ x = 20} }$ Now, we can know the value of all three angles by putting x 1ST angle $\implies \sf (2x + 5)\\ \\ \implies \sf 2(20) + 5 \\ \\ \implies \sf \boxed{\pink{ 45^\circ}}$ 2nd angle $\implies \sf (4x+10)\\ \\ \implies \sf 4\times20 + 10 \\\\\implies \sf \boxed{\pink {90^\circ}}$ 3rd angle $\implies \sf (3x-15) \\ \\\implies \sf 3\times20 -15 \\ \\ \implies \sf \boxed{\pink{ 45^\circ}}$ Here, One angle is of 90°. Hence, it is right angled triangle Other TWO angles are of 45°. Hence, it is isosceles triangle. Hence, This triangle has two angles of 45° and one of 90°. So, it is a Right angled isosceles triangle.

34. The measures of the angles of a triangle are (2x + 5)º. (4x + 10)° and(3x - 15). What type of triangle is it?(1) Scalene right angled triangle(2) Scalene obtuse angled triangle(3) Right angled isosceles triangle(4) Acute angled isosceles triangle

Answer»

Answer :

Right angled isosceles triangle.

Solution :

Given :

(2x + 5)º, (4x + 10)° and (3x - 15)° are angles of a triangle.

To Find :

Type of triangle.

Let's solve ,

We know that ,

SUM of all angles of a triangle = 180°

So,

(2x + 5)º + (4x + 10)° + (3x - 15)° = 180°

➩ 2x + 5 + 4x + 10 + 3x - 15 = 180°

$\implies \sf 9x + \cancel{15}\: \: \cancel{-15}$ = 180°

$\implies \sf <klux>X</klux> = \dfrac{180}{9} \\ \\ \implies \sf \red \boxed{\sf{ x = 20} }$

Now, we can know the value of all three angles by putting x

1ST angle

$\implies \sf (2x + 5)\\ \\ \implies \sf 2(20) + 5 \\ \\ \implies \sf \boxed{\pink{ 45^\circ}}$

2nd angle

$\implies \sf (4x+10)\\ \\ \implies \sf 4\times20 + 10 \\\\\implies \sf \boxed{\pink {90^\circ}}$

3rd angle

$\implies \sf (3x-15) \\ \\\implies \sf 3\times20 -15 \\ \\ \implies \sf \boxed{\pink{ 45^\circ}}$

Here,

One angle is of 90°. Hence, it is right angled triangle
Other TWO angles are of 45°. Hence, it is isosceles triangle.

Hence,

This triangle has two angles of 45° and one of 90°. So, it is a Right angled isosceles triangle.