If in triangle ABC angle A and B are exactly the same, but angle C is half as large as angle A, how much is each angle equal to?
To find the value of each angle of the triangle use the property that the sum of the angles of a triangle is equal to 180 degrees.
As angle C is half as large as angle A and A = B, we can write the three angles of the triangle in terms of C as C, 2C and 2C.
C + 2C + 2C = 5C = 180
=> C = 36
A = 36*2 = 72 = B
The angles of the triangle are A = 72 degrees, B = 72 degrees and C = 36 degrees.
The sum of the three angles in a triangle add to 180 degrees. So if two of the angles are equal and the third is half as much as one, the developed equation is x+x+.5x=180. Combining like terms, 2.5x=180. Divide both sides by 2.5 and x=72. Angle A and B will be 72 degrees and angle C is 36 degrees.