Question

An exterior angel of a triangle is 130degree and its interior opposite angeles are in the ratio of 7:6 find the meaure of each angel of the tringle

Answer 1

$\huge\red{Answer\:is}$

Let the angles are 7x and 6x

ATQ
$7x + 6x = 130 \\ 13x = 130 \\ x = \frac{130}{13} \\ x = 10 \\ so \: angles \: are7 \times 10 = 70 \\ second \: angle \: is \: 6 \times 10 = 60 \\ third \: angle \: is \: 180 - 70 - 60 \\ = 50$
Hope it helps you

Answer 2

$\Large\bold{\underline{\sf{\red{AnsWer\::}}}}$

• Given :

Exterior angle of triangle = 130°

Interior opposite angles are in ratio of 7:6

• To Find :

Each angle of triangle

• Solution :

➡ We know that :

$\small\bold{\sf{\pink{Exterior\:angle\:of\:∆\:=\:Sum\:of\:opposite\:interior\:angles}}}$

▶Let the angles be " x " . Now , ATQ :

= $\sf 7x \:+ \:6x \:=\: 130°$

= $\sf 13x\: =\: 130°$

= $\sf x\:=\: \dfrac{130°}{13}$

= $\sf x\:=\: 10°$

• Interior Opposite Angles :

Angle A = 7x = 7(10) = 70°

Angle B = 6x = 6(10) = 60°

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Now , let us find third angle of the triangle :

$\small\bold{\sf{\pink{Angle\:sum\:property\:of\:∆\:=\:180°}}}$

= $\sf 70° \:+\: 60°\: +\: \angle ACB\:= \:180°$

= $\sf 130° \:+ \: \angle ACB\:=\: 180°$

= $\sf \angle ACB\:=\:180°\:-\:130°$

= $\sf \angle ACB\:=\:50°$

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• Angles of Triangle are : 70° , 60° and 50°

☯ For Figure , Refer to the attachment .

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