Angles of a triangle

Question

The second angle of a triangular kite is 4 times as large as the first. The third angle is 5 degrees more than the sum of the other two angles. Find the measures of the other two angles

Answer 1

Call angle 1 ... x

Angle 2  = 4x

Angle 3 = x + 4x + 5 = 5x + 5

 

The sum of the 3 angles of a triangle is 180 so...

 

x + 4x + 5x + 5 = 180

10x + 5 = 180

10x = 175

x = 17.5 degrees for angle 1

 

Angle 2 = 4x = 4(17.5) = 70 degrees

 

Angle 3 = 5x + 5 = 5(17.5) + 5 = 92.5 degrees