Answer:
The measure of angle b (angle dbc) is [tex]54\°[/tex]
The measure of angle c is [tex]59\°[/tex]
The measure of angle d is [tex]67\°[/tex]
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
so
[tex]x+y+z=180\°[/tex] -----> equation A
[tex]x=y-5[/tex] -----> equation B
[tex]z=y+8[/tex] ----> equation C
Substitute equation B and equation C in equation A and solve for y
[tex](y-5)+y+(y+8)=180\°[/tex]
[tex]3y+3=180\°[/tex]
[tex]3y=177\°[/tex]
[tex]y=59\°[/tex]
Find the value of x
[tex]x=59\°-5\°=54\°[/tex]
Find the value of z
[tex]z=59\°+8\°=67\°[/tex]
The measures of each angle of the triangle are
The measure of angle b (angle dbc) is [tex]54\°[/tex]
The measure of angle c is [tex]59\°[/tex]
The measure of angle d is [tex]67\°[/tex]
