Question

The acute angles of a right triangle is in the ratio 2 : 1. The smallest angle is ?

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Answer 1

Step-by-step explanation:

The acute angles of the right angled triangle are x and 2x.

Hence x+2x = 3x = 90, or

x = 90/3 = 30.

So the two acute angles of the right angled triangle are 30 deg and 60 deg. Answer

hope it helps!!

Answer 2

Answer :

• Smallest angle = 30°

Given :

• The triangle is right angled triangle .
• The ratio of acute angles = 2:1 .

To find :

• The smallest angle

Solution :

By the angle sum property of a triangle ,

Angle 1 + angle 2 + Angle 3 = 180° _____(1)

Let angle 1 = right angle = 90° and the common ratio between angle 2 and angle 3 be x .

$\therefore \tt \angle2 = 2x \: and \: \angle3 = x$

Substituting these values in equation 1 .

90° + 2x + x = 180°

⇢90° + 3x = 180°

⇢3x = 180° -90°

⇢3x = 90°

⇢x = 90° / 3

⇢x = 30°

$\boxed{\therefore \sf \angle2 = 2 \times 30 = {60}^{ \circ} \: and \: \angle3 = {30}^{ \circ} }$

Hence , the smallest angle is 30° .

______________________

• A triangle that has one angle 90° is called a right angled triangle .

• According to angle sum property of a triangle , the sum of all interior angles of a triangle sums up to 180° .