The sum of the two angles in a triangle is 95 ∘ and their difference is 25 ∘ . Then which of the following are true? Options: A . &nbsp One of the angles is 35 ∘ . B . &nbsp One of the angles is 50 ∘ C . &nbsp One of the angles is 60 ∘ D . &nbsp One of the angles is 85 ∘

Answer: Option A : A, C, and D Let the two angles be x and y . So, x + y = 95 ∘ ⇒ x = 95 ∘ − y ⋅ ⋅ ⋅ (i) and, x − y = 25 ∘ ⋅ ⋅ ⋅ (ii) Substitute (i) in (ii), ⇒ 95 ∘ − y − y = 25 ∘ ⇒ 95 ∘ − 2 y = 25 ∘ ⇒ y = 95 ∘ − 25 ∘ 2 ⇒ y = 35 ∘ So, x = 95 ∘ − 35 ∘ ⇒ x = 60 ∘ Third angle is 180 ∘ − 95 ∘ = 85 ∘ So, the angles are 35 ∘ , 60 ∘ and 85 ∘ .

The sum of the two angles in a triangle is 95∘ and their differenc

Question

The sum of the two angles in a triangle is $95^{\circ}$ and their difference is $25^{\circ}$ . Then which of the following are true?

Options:

A . One of the angles is

35^{\circ}

B . One of the angles is

50^{\circ}

C . One of the angles is

60^{\circ}

D . One of the angles is

85^{\circ}

Answer: Option A
:
A, C, and D

Let the two angles be $x$ and $y$ .

So, $x + y = 95^{\circ}$
$\Rightarrow x = 95^{\circ} - y$ $\cdot \cdot \cdot$ (i)

and, $x - y = 25^{\circ}$ $\cdot \cdot \cdot$ (ii)
Substitute (i) in (ii),
$\Rightarrow 95^{\circ} - y - y = 25^{\circ}$

$\Rightarrow 95^{\circ} - 2 y = 25^{\circ}$
$\Rightarrow y = \frac{95^{\circ} - 25^{\circ}}{2}$
$\Rightarrow y = 35^{\circ}$

So, $x = 95^{\circ} - 35^{\circ}$

$\Rightarrow$ $x = 60^{\circ}$

Third angle is $180^{\circ} - 95^{\circ} = 85^{\circ}$

So, the angles are $35^{\circ}$ , $60^{\circ}$ and $85^{\circ}$ .

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