Question

angles b.c. and d equal 180
angle b is 25
angle c is 3x
angle d is 3x + 5
what do angles c and d equal

Answer 1

To solve for angles \( c \) and \( d \), we know from the problem statement that angles \( b \), \( c \), and \( d \) sum up to \( 180^\circ \). We can express this as:

\[
b + c + d = 180^\circ
\]

Given:
- \( b = 25^\circ \)
- \( c = 3x \)
- \( d = 3x + 5 \)

Substituting the values of \( b \), \( c \), and \( d \) into the equation, we get:

\[
25 + 3x + (3x + 5) = 180
\]

Simplifying this equation:

\[
25 + 3x + 3x + 5 = 180
\]

Combine like terms:

\[
25 + 5 + 6x = 180
\]
\[
30 + 6x = 180
\]

Now, subtract \( 30 \) from both sides:

\[
6x = 150
\]

Now, divide by \( 6 \):

\[
x = 25
\]

Now that we have \( x \), we can find angles \( c \) and \( d \):

\[
c = 3x = 3(25) = 75^\circ
\]
\[
d = 3x + 5 = 3(25) + 5 = 75 + 5 = 80^\circ
\]

Thus, the angles are:
- Angle \( c = 75^\circ \)
- Angle \( d = 80^\circ \)