Question

If the angles of a triangle are in the ratio 3:9:6, then the triangle is: a) acute b) right c) obtuse d) straight​

Answer 1

✬ Right Triangle ✬

Step-by-step explanation:

Given:

• Angles of triangle are in ratio 3 : 9 : 6.

To Find:

• Which type of triangle is this?

Solution: Let x be the common in given ratio. Therefore,

➟ Angles are - 3x , 9x ,6x

As we know that

★ Sum of all angles of ∆ = 180° ★

$\implies{\rm }$ 3x + 9x + 6x = 180°

$\implies{\rm }$ 12x + 6x = 180°

$\implies{\rm }$ 18x = 180°

$\implies{\rm }$ x = 180/18

$\implies{\rm }$ x = 10°

So, measure of angles are

➭ 3x = 3(10) = 30°

➭ 9x = 9(10) = 90°

➭ 6x = 6(10) = 60°

This triangle is a right angled triangle. (Option B is correct)

• Reason behind this •ᴗ• = This is a triangle with one right angle (or an angle that measures 90°) and two acute angles, where an acute angle is an angle that measures less than 90°.

Answer 2

$\bf{\underline{\underline{Question:-}}}$

If the angles of a triangle are in the ratio 3:9:6, then the triangle is.

• a) acute
• b) right
• c) obtuse
• d) straight

$\bf{\underline{\underline{Given:-}}}$

• angles of a triangle are in the ratio 3:9:6

$\bf{\underline{\underline{To\:Find:-}}}$

• The ∆ is ?

$\bf{\underline{\underline{By \:The \: Triangle\: Property:-}}}$

• Sum of all angles of Triangle is 180°

$\bf{\underline{\underline{Solution:-}}}$

Let,

• All the given ratios be in the form of X

$\sf :→ 3x + 9x +6x=180°$

$\sf :→ 18x = 180°$

$\sf :→ x = 180°/18$

$\sf :→ x = 10°$

$\bf{\underline{\underline{Hence:-}}}$

• The angle of triangle are

→ First angle = 3x = 3 × 10 = 30°

→ Second angle = 9x = 9 × 10 = 90°

→ Third angle = 6x = 6 × 10 = 60°

$\large{\boxed{\underline{\red{\tt{The\:Triangle\:is \:Right\: angle\: triangle}}}}}$

$\bf{\underline{\underline{Reason:-}}}$

• We know the that if the two angle of ∆ is less than 90° and one is right angle then the triangle is Right angle triangle .