Question

In a triangle, the second angle is three times the first angle, and the first angle is half of the third angle, what is the value of the first angle?​

Answer 1

Answer:

30°

Step-by-step explanation:

Let the third angle be ' x '

First angle = 1/2( x ) = x/2

Second angle = 3( first angle ) = 3[ 1/2( x ) ] = 3x/2

Third angle = x

∵ The Sum of all angles of a triangle is equal to 180°.

By Angle sum property of a triangle.

∴ a + b + c = 180°

⇒  x/2 + 3x/2 + x = 180°

⇒            4x/2 + x = 180°

⇒      4x/2 + 2x/2 = 180°

⇒                 6x/2 = 180°

⇒                     3x = 180°

⇒                       x = 180° / 3

⇒                      x = 60°

First angle = x/2

                 = 60° / 2

                 = 30°

∴ The value of the first angle is 30°.

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