Question

The sum of two angles of a triangle is 116degree and their difference is 24degree . Find the measure of each angle of the triangle

Answer 1

Given:

• The sum of two angles of a triangle is 116°.
• & The difference b/w these two angles of a triangle is 24°.

To find:

• The measure of each angle of the ∆?

Solution: Let the two angles of the triangle be ∠A and ∠B respectively.

The sum of these two angles,

➟ ∠A + ∠B = 116°⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ —eqⁿ. ( I )

The difference b/w two angles,

➟ ∠A – ∠B = 24°

➟ ∠A = 24° + ∠B⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ —eqⁿ. ( II )

As we know that,

• Sum of all angles of a triangle is 180°.

★ ∠A + ∠B + ∠C = 180° ★

⇥ 116° + ∠C = 180° ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀[From eqⁿ ( I )]

⇥ ∠C = 180° – 116°

⇥ ∠C = 64°

⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━

• Putting the value of eqⁿ ( II ) in eqⁿ ( I ) :

➟ ∠A + ∠B = 116°

➟ 24° + ∠B + ∠B = 116° ⠀⠀⠀⠀⠀⠀⠀[From eqⁿ ( II )]

➟ 24° + 2∠B = 116°

➟ 2∠B = 116° – 24°

➟ 2∠B = 92°

➟ ∠B = 92/2

➟ ∠B = 46°

⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━

• Putting the value of ∠B in eqⁿ. ( II ) :

⇥ ∠A = 24° + ∠B

⇥ ∠A = 24° + 46°

⇥ ∠A = 70°

Therefore, the measure of each angle is 70°, 46° and 64° respectively$.$

Answer 2

Answer:

Given :-

• The sum of two angles of a triangle is 116° degree and their difference is 24 degree.

To Find :-

• What is the measure of each angles of the triangle.

Solution :-

Let,

$\mapsto \bf First\: Angle =\: \angle{A}$

$\mapsto \bf Second\: Angle =\: \angle{B}$

According to the question,

$\bigstar$ The sum of two angles of a triangle is 116°.

$\footnotesize\implies \bf First\: Angle + Second\: Angle =\: 116^{\circ}$

$\implies \sf \angle{A} + \angle{B} =\: 116^{\circ}$

$\implies \sf\bold{\purple{\angle{A} + \angle{B} =\: 116^{\circ}\: ------\: (Equation\: No\: 1)}}$

Again,

$\bigstar$ The difference between two angles is 24°.

$\footnotesize \implies \bf First\: Angle - Second\: Angle =\: 24^{\circ}$

$\implies \sf \angle{A} - \angle{B} =\: 24^{\circ}$

$\implies \sf\bold{\purple{\angle{A} - \angle{B} =\: 24^{\circ}\: ------\: (Equation\: No\: 2)}}$

Now, 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,

$\implies \sf \angle{A} + \angle{B} + \angle{C} =\: 180^{\circ}$

$\implies \sf 116^{\circ} + \angle{C} =\: 180^{\circ}\: \: \bigg\lgroup \small\sf\bold{From\: equation\: no\: 1}\bigg\rgroup$

$\implies \sf \angle{C} =\: 180^{\circ} - 116^{\circ}$

$\implies \sf\bold{\red{\angle{C} =\: 64^{\circ}}}$

Now, by putting the value of equation no 2 in the equation no 1 we get,

$\implies \sf \angle{A} + \angle{B} =\: 116^{\circ}$

$\implies \sf 24^{\circ} + 2\angle{B} =\: 116^{\circ}$

$\implies \sf 2\angle{B} =\: 116^{\circ} - 24^{\circ}$

$\implies \sf 2\angle{B} =\: 92^{\circ}$

$\implies \sf \angle{B} =\: \dfrac{\cancel{92^{\circ}}}{\cancel{2}}$

$\implies \sf \angle{B} =\: \dfrac{46^{\circ}}{1}$

$\implies \sf\bold{\red{\angle{B} =\: 46^{\circ}}}$

Again, by putting the value of ∠B in the equation no 1 we get,

$\implies \sf \angle{A} + \angle{B} =\: 116^{\circ}$

$\implies \sf \angle{A} + 46^{\circ} =\: 116^{\circ}$

$\implies \sf \angle{A} =\: 116^{\circ} - 46^{\circ}$

$\implies \sf\bold{\red{\angle{A} =\: 70^{\circ}}}$

${\footnotesize{\bold{\underline{\therefore\: The\: measure\: of\: each\: angles\: of\: a\: triangle\: is\: 70^{\circ}\: , 46^{\circ}\: and\: 64^{\circ}\: respectively\: .}}}}$