Together the measures of <B, <C, and <D equal 180 degrees. The angles have the following measures:
m<B = 25 degrees
m<C= (3x)degrees
and m<D = (3x+5) degrees.
What are the measures of <C and <D?
Since the sum of the measures of all three angles is equal to 180 degrees, we have:
25 + 3x + 3x + 5 = 180
Combining like terms, we get:
6x + 30 = 180
Subtracting 30 from both sides:
6x = 150
Dividing both sides by 6:
x = 25
Now, we can substitute x back into the expressions for angle C and angle D:
m<C = 3x = 3(25) = 75 degrees
m<D = 3x + 5 = 3(25) + 5 = 75 + 5 = 80 degrees
Therefore, angle C measures 75 degrees and angle D measures 80 degrees.