Question

. If the measures of the three angles of a triangle are (3x + 15), (5x – 15), and (2x + 30), what is the measure of each angle?

Answer 1

       $\underline{\bold{Solution:}}$

       $\text{It is given that }(3x+15),(5x-15) \text{ and }(2x + 30) \text{ are angles of a triangle}$

       $\text{We know that angles of a triangle sum upto }180^{\circ}$

$\implies 3x + 15 + 5x - 15 + 2x + 30 = 180$

$\implies 10x + 30 = 180$

$\implies 10x = 180 - 30$

$\implies 10x = 150$

$\implies x = \dfrac{150}{10}$

$\implies x = 15$

 $\therefore\text{ }\text{ The angles are:}$

       $3x + 15$                $5x - 15$                $2x + 30$

$\implies 3(15) + 15$     $\implies 5(15) - 15$    $\implies 2(15) + 30$

$\implies 45 + 15$         $\implies 75 - 15$         $\implies 30 + 30$

$\implies \boxed{60^\circ}}$             $\implies \boxed{60^{\circ} }$            $\implies \boxed{60^{\circ} }$  

Answer 2

Answer:

Given :-

• The measure of the three angles of a triangle are (3x + 15)°, (5x - 15)° and (2x + 30)°.

To Find :-

• What is the measure of each angles.

Solution :-

Let,

➲ First angle of triangle = (3x + 15)°

➲ Second angle of triangle = (5x - 15)°

➲ Third angle of triangle = (2x + 30)°

As we know that :

$\footnotesize\bigstar\: \: \sf\boxed{\bold{\pink{Sum\: of\: all\: angles\: of\: triangle =\: 180^{\circ}}}}\: \: \bigstar$

According to the question by using the formula we get,

$\implies \sf 3x + 15^{\circ} + 5x - 15^{\circ} + 2x + 30^{\circ} =\: 180^{\circ}$

$\implies \sf 3x + 5x + 2x {\cancel{+ 15^{\circ}}} {\cancel{- 15^{\circ}}} + 30^{\circ} =\: 180^{\circ}$

$\implies \sf 10x + 30^{\circ} =\: 180^{\circ}$

$\implies \sf 10x =\: 180^{\circ} - 30^{\circ}$

$\implies \sf 10x =\: 150^{\circ}$

$\implies \sf x =\: \dfrac{15\cancel{0}^{\circ}}{1\cancel{0}}$

$\implies \sf\bold{\purple{x =\: 15^{\circ}}}$

Hence, the required measure of each angles are :

❒ First Angle Of Triangle :

⇒ First Angle = (3x + 15)°

⇒ First Angle = {3(15°) + 15}°

⇒ First Angle = (45° + 15°)

➠ First Angle = 60°

❒ Second Angle Of Triangle :

⇒ Second Angle = (5x - 15)°

⇒ Second Angle = {5(15°) - 15}°

⇒ Second Angle = (75° - 15°)

➠ Second Angle = 60°

❒ Third Angle Of Triangle :

⇒ Third Angle = (2x + 30)°

⇒ Third Angle = {2(15°) + 30}°

⇒ Third Angle = (30° + 30°)

➠ Third Angle = 60°

∴ The measure of each angles of a triangle are 60°, 60° and 60° respectively.