Question

The two angles of a right angle triangle are in the ratio 2:3.find the measure of each of these angles​

Answer 1

Answer:

The angles of the triangle are 54°, 36° and 90°.

Step-by-step explanation:

Given :

Triangle is a = Right angled triangle

Ratio of two angles = 2 : 3

To find :

Measure of one angle

Solution :

Let the angles be -

• One as 2x
• Second as 3x

As It is a Right angled triangle, the third angle will be 90°

According to the Angle Sum property of triangle, sum of all the angles in a triangle is 180°.

$\longrightarrow$ 90 + 2x + 3x = 180

$\longrightarrow$ 90 + 5x = 180

$\longrightarrow$ 5x = 180 - 90

$\longrightarrow$ 5x = 90

$\longrightarrow$ x = 90/5

$\longrightarrow$ x = 18

$\rule{300}{1.5}$

★ Value of 2x

$\longrightarrow$ 2(18)

$\longrightarrow$ 36

First angle = 36°

$\rule{300}{1.5}$

★ Value of 3x

$\longrightarrow$ 3(18)

$\longrightarrow$ 54

Second Angle = 54°

$\therefore$ The angles of the triangle are 54°, 36° and 90°.

Answer 2

Given,

The two angles of a right angle triangle are in the ratio 2:3.

To find out,

The measure of each angle.

Solution:

Right angle triangle: A triangle in which one angle is 90°.

Let us take the triangle be ABC and angles <A,<B,<C.

Let the angles be <A = 2x°, <B=90° and <C = 3x°.

Now,

By triangle sum theory:sum of 3 angles of a triangle is 180°.

That is, <A + <B + <C = 180°

2x°+90°+3x° = 180°

5x° + 90° = 180°

5x° = 180°-90°

5x° = 90°

x = 90/5

x = 18°

Therefore the <A = 2x = 2(18)=36° and <C = 3x = 3(18) = 54°

Verification:

<A + <B + <C = 180°

36°+90°+54° = 180°

180° = 180°

L.H.S = R.H.S