Question

if one of the exterior qngle of a triangle is 120° and the interior opposite angle are in the ratio 3 : 7 , find their measure​

Answer 1

$\red{\mathfrak {Question:-}}$

• If one of the exterior angle of a triangle is 120° and the interior opposite angle are in the ratio 3:7. Find their measure.

$\green{\mathfrak {Answer:-}}$

• We know that, according to exterior angle property of a triangle,

• $\fbox{Exterior angle of a triangle = Sum of angles opposite to the interior angles.}$

• Let the angles be x.

• One angle will be 3x and the other angle will be 7x.

• $\therefore { 3x + 7x = 120° }$

• 10x = 120°

• ${x = \frac{120}{10}}$

• $\therefore { x = 12° }$

• One angle = 3x = 3 x 12 = 36°

• Other angle = 7x = 7 x 12 = 84°

$\orange{\mathfrak {Conclusion:-}}$

• $\fbox{Measure of Angles are 36° and 84°.}$

Answer 2

Answer:

Given :-

• One of the exterior angles of a triangle is 120° and the interior opposite angles are in the ratio of 3 : 7.

To Find :-

• What are the angles.

Solution :-

Let, the first angles of a triangle be 3x

And, the second angles of a triangle will be 7x

As we know that,

$\bigstar\: \sf\bold{Sum\: of\: all\: angles\: of\: a\: triangle\: =\: 120^{\circ}}$

According to the question by using the formula we get,

⇒ $\sf 3x + 7x =\: 120^{\circ}$

⇒ $\sf 10x =\: 120^{\circ}$

⇒ $\sf x =\: \dfrac{\cancel{120^{\circ}}}{\cancel{10}}$

➠ $\sf\bold{\pink{x =\: 12^{\circ}}}$

Hence, the required angles are :

$\longmapsto$ First angles of a triangle :

$\implies$ $\sf 3x$

$\implies$ $\sf 3 \times 12^{\circ}$

$\implies$ $\sf\bold{\red{36^{\circ}}}$

And,

$\longmapsto$ Second angles of a triangle :

$\implies$ $\sf 7x$

$\implies$ $\sf 7 \times 12^{\circ}$

$\implies$ $\sf\bold{\red{84^{\circ}}}$

$\therefore$ The angles of a triangle is 36° and 84° respectively.

${\underline{\boxed{\mathcal{\pmb{\quad VERIFICATION :-\quad}}}}}$

↦ $\sf 3x + 7x =\: 120^{\circ}$

By putting x = 12° we get,

↦ $\sf 3 \times 12^{\circ} + 7 \times 12^{\circ} =\: 120^{\circ}$

↦ $\sf 36^{\circ} + 84^{\circ} =\: 120^{\circ}$

↦ $\sf\bold{\purple{120^{\circ} =\: 120^{\circ}}}$

➦ LHS= RHS

Hence, Verified .