Question

give me the answer with a full explanation

Answer 1

Given Question

In triangle ABC, ∠A + ∠B = 125° and ∠B + ∠C = 150°. Find all the angles of triangle ABC.

$\large\underline{\sf{Solution-}}$

Given that,

In triangle ABC

$\purple{\rm :\longmapsto\:\angle A + \angle B = 125 \degree \: - - - (1) }$

$\purple{\rm :\longmapsto\:\angle B + \angle C = 150 \degree \: - - - (2)}$

We know,

Sum of all interior angles of a triangle is supplementary.

$\purple{\rm :\longmapsto\:\angle A + \angle B + \angle C = 180\degree }$

On adding equation (1) and (2), we get

$\purple{\rm :\longmapsto\:\angle A + \angle B + \angle B + \angle C = 125\degree + 150 \degree \:}$

$\purple{\rm :\longmapsto\:\angle A + \angle B + \angle C + \angle B = 275\degree \:}$

$\purple{\rm :\longmapsto\:180\degree + \angle B = 275\degree \:}$

$\purple{\rm :\longmapsto\:\angle B = 275\degree - 180\degree \:}$

$\purple{\rm :\longmapsto\:\angle B = 95\degree \:}$

On substituting the value in equation (1) and (2), we get

$\purple{\rm :\longmapsto\:\angle A + 95\degree = 125\degree }$

$\purple{\rm :\longmapsto\:\angle A = 125\degree - 95\degree }$

$\purple{\rm :\longmapsto\:\angle A = 30\degree }$

Also, from equation (2), we get

$\purple{\rm :\longmapsto\:95\degree + \angle C = 150\degree }$

$\purple{\rm :\longmapsto\:\angle C = 150\degree - 95\degree }$

$\purple{\rm :\longmapsto\:\angle C = 55\degree }$

Hence,

$\begin{gathered}\begin{gathered}\bf\: \rm\implies \:\begin{cases} &\sf{\angle A = 30\degree } \\ \\ &\sf{\angle B = 95\degree } \\ \\ &\sf{\angle C = 55\degree } \end{cases}\end{gathered}\end{gathered}$

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MORE TO KNOW

1. Exterior angle of a triangle is equals to sum of interior opposite angles.

2. Angle opposite to equal sides are equal.

3. Sides opposite to equal angles are equal.

4. Angle opposite to longest side is always greater.

5. Side opposite to greater angle is always longest.

Answer 2

Question :-

In $\triangle$ ABC, $\angle$ A + $\angle$ B = 125° and $\angle$ B + $\angle$ C = 150°. Find all the angles of $\triangle$ ABC.

Answer :-

$\rm:\longmapsto{\angle A = 30°}$

$\rm:\longmapsto{\angle B = 95°}$

$\rm:\longmapsto{\angle C = 55°}$

Step by step explanation :-

We have given that,

$\rm:\longmapsto{\angle A + \angle B = 125° - - - - (1)} \\ \\ \rm:\longmapsto{\angle B + \angle C = 150° - - - - (2)}$

Adding equation (1) and equation (2)

$\rm:\longmapsto{ \angle A + \angle B + \angle B + \angle C = 125 \degree + 150 \degree} \\ \\\rm:\longmapsto{ \angle A + \angle B + \angle C + \angle B=275\degree} \: \: \: \: \: \: \: \: \: \: \: \: \:$

We know that,

$\small\rm:\longmapsto{\angle A + \angle B + \angle C = 180° \: \: \: \: .... (\because Sum \: of \: all \: angles \: o f \: t riangle \: is \: 180°) }$

Now,

$\rm:\longmapsto{180 \degree + \angle B = 275 \degree} \\ \\\rm:\longmapsto{\angle B = 275 \degree - 180 \degree} \\ \\ \bf:\longmapsto \red{\angle B = 95 \degree} \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Substituting $\angle$ B = 95° in equation (1)

$\rm:\longmapsto{\angle A + \angle B = 125°} \\ \\ \rm:\longmapsto{\angle A +95 \degree= 125°} \\ \\ \rm:\longmapsto{\angle A = 125° - 95 \degree} \\ \\ \bf:\longmapsto \red{\angle A = 30 \degree} \: \: \: \: \: \: \: \: \: \: \:$

Substituting $\angle$ B = 95° in equation (2)

$\rm:\longmapsto{\angle B+ \angle C = 150°} \\ \\ \rm:\longmapsto{95 \degree+ \angle C = 150°} \\ \\ \rm:\longmapsto{\angle C = 150° - 95 \degree} \\ \\\bf:\longmapsto \red{ \angle C = 55 \degree} \: \: \: \: \: \: \: \: \: \: \:$

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(2) in triangle abc angle a + angle b is equal to 125 degree and angle b + angle c is equal to 150 degree find all the angles of a triangle ABC

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