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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?

User TPoy
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1 Answer

7 votes

Answer:

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\°

User Kirill Rakhman
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