An isosceles triangle has angle A 30 degrees greater than angle B. Find all angles of triangle?
We know that since we have an isosceles triangle that two of the sides and therefore the angles will be equal. The third angle we are told is 30 degrees more than the one of the others.
Let's call the equal angles' measurement x
The three angles can be represented by:
x + 30
The three angles will add up to 180:
x + x + x +30 = 180
Solving for x:
3x + 30 = 180
3x = 150
x = 50
So our 3 angles are 50, 50, 80
We'll recall the fact that an isosceles triangle has two equal angle. Since the angle A is 30 degrees greater than B, then the equal angles are B and C.
We also know that the sum of the angles in a triangle is of 180 degrees, such as:
A + B + C = 180
A = B + 30
B = C
B + 30 + B + B = 180
3B + 30 = 180
3B = 180 - 30
3B = 150
B = 50 degrees
But B=C=>C=50 degrees.
A = B + 30 = 50+30 = 80 degrees.
Therefore, the requested angles of isosceles triangle ABC are: A=80, B=50, C=50 degrees.