one angle of a triangle is 6 degrees less than a second angle, while the third angle is 24 degrees more than the second angle.

Question

write an equation and solve.

Answer 1

Let x = the measure of the 2nd angle:

• The first angle of a triangle is 6 degrees less than the second angle: x-6
• The third angle is 24 degrees more than the second angle: x+24

 

The three angles must add up to 180^o:

x-6 + x + x+24 = 180^o

3x + 18 = 180^o

3x = 162^o

x = 54^o

 

The other angles are x-6 = 48^o and x+24 = 78^o

 

48^o + 54^o + 78^o = 180^o