Answer
The measure of each angles is $ 25^{\circ} , 35^{\circ} $ and $ 120^{\circ} $.
Work Step by Step
let the angles of a triangle are $ A,B $ and $C$.
Sum of all angles of a triangle is $ =180^{\circ} $.
$ A+B+C =180^{\circ} $ ... (1)
one angle of a triangle measures $ 10 ^{\circ} $ more than the second angle.
In the equation form.
$ A=B+10^{\circ} $ ... (2)
The measure of the third angle is twice the sum of the measures of the first two angles.
in the equation form.
$ C=2(A+B) $ ... (3)
Substitute the value of $ A $ from equation (2) to equation (3).
$ C=2(B+10^{\circ}+B) $
$ C=2(2B+10^{\circ}) $
$ C=4B+20^{\circ} $ ... (4)
Substitute the values of $ A $ and $ C $ from equation (2) and (4) into equation (1).
$ B+10^{\circ}+B+4B+20^{\circ} =180^{\circ} $
Simplify.
$ 6B+30^{\circ} =180^{\circ} $
$ 6B =180^{\circ}-30^{\circ} $
$ 6B =150^{\circ} $
$ B =\frac{150^{\circ}}{6} $
$ B =25^{\circ} $.
Substitute the value of $ B $ into equation (2).
$ A=25^{\circ}+10^{\circ} $
$ A=35^{\circ} $.
Now Substitute the value of $ B $ into equation (4).
$ C=4(25^{\circ})+20^{\circ} $
$ C=100^{\circ}+20^{\circ} $
$ C=120^{\circ} $.
