Question

One angle of a triangle is one third of the other and the third angle is 19° more than the greater of two angles. Find the three angles of the triangle.

Answer 1

Let the first angle be x.


So according to the question,
second angle = x/3

Now third angle is 19 more than the greater
Since, x > x/3

So, third angle = 19 + x

So now we can apply the angle sum property of triangle.
By angle sum property,

x + x/3 + (x + 19) = 180°

=>
$x + \frac{x}{3} + x + 19 = 180 \\ \\ = > \frac{3x}{3} + \frac{x}{3} + \frac{3x}{3} + \frac{57}{3} = 180 \\ \\ = > \frac{7x + 57}{3} = 180 \\ \\ = > 7x + 57 = 180 \times 3 \\ \\ = > 7x = 540 - 57 \\ \\ = > 7x = 483 \\ \\ = > x = \frac{483}{7} \\ \\ = > x = 69$
Now, x = 69°

So second angle = x/3 = 69/3 = 23°

Third angle = x + 19 = 69 + 19 = 88°


First angle = 69°
Second = 23°
Third = 88°

Hope it helps dear friend ☺️