Question

Angle dbc measures 5 degrees less than angle c and angle d measures 8 degrees more than angle c. What are the measures of each angle of the triangle?

Answer 1

The measure of angle b (angle dbc) is
`54\°`

The measure of angle c is
`59\°`

The measure of angle d is
`67\°`

Explanation:

Let

x-----> measure of angle b (angle dbc)

y----> measure of angle c

z----> measure of angle d

Remember that

The sum of the internal angles of a triangle must be equal to 180 degrees

so

`x+y+z=180\°` -----> equation A

`x=y-5` -----> equation B

`z=y+8` ----> equation C

Substitute equation B and equation C in equation A and solve for y

`(y-5)+y+(y+8)=180\°`

`3y+3=180\°`

`3y=177\°`

`y=59\°`

Find the value of x

`x=59\°-5\°=54\°`

Find the value of z

`z=59\°+8\°=67\°`

The measures of each angle of the triangle are

The measure of angle b (angle dbc) is
`54\°`

The measure of angle c is
`59\°`

The measure of angle d is
`67\°`