Mathematics: 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--It s in the picture, desmos will help for graphing....

Angle dbc measures 5 degrees less than angle

hendo617

04.01.2022

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

The measure of angle c is $59\°$

The measure of angle d is $67\°$

Step-by-step 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

$x+y+z=180\°$ -----> 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 $67\°$

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