Question

In any triangle, the three angles add up to 180°. In my triangle, the first angle is twice the second angle, and the second angle is 30° larger than the third. What are the angles in a triangle, in order?

Answer 1

Therefore the angles of the triangle are 52.5°, 105°,49.5°.

Explanation:

Triangle:

• The sum of the angle of triangle = 180°

• Heron's formula the area of triangle =
  `√(s(s-a)(s-b)(s-c))`

s= semi-perimeter
`=(a+b+c)/(2)`

Given that , first angle is twice the second angle, and the second angle is 30° larger than the third angle.

Consider the second angle of the triangle be x.

Then first angle = twice the second angle

=2× second angle

=2x

The third angle+30° = second angle

⇒third angle= second angle -30°

= x- 30°

We know that,

First angle + second angle+ Third angle = 180°

⇒2x+x+x-30°= 180°

⇒4x = 180° +30°

⇒4x=210°

`\Rightarrow x= (210^\circ)/(4)`

⇒x=52.5°

Therefore the angles of the triangle are 52.5°, (2×52.5°),(52.5°-30°)

=52.5°, 105°,49.5°