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

Answer:

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

Step-by-step explanation:

Triangle:

• The sum of the angle of triangle = 180°

• Heron's formula the area of triangle = $\sqrt{s(s-a)(s-b)(s-c)}$

s= semi-perimeter $=\frac{a+b+c}{2}$

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°

$\Rightarrow x= \frac{210^\circ}{4}$

⇒x=52.5°

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

                                                                    =52.5°, 105°,49.5°