Together the measures of <B, <C, and <D equal 180 degrees. The angles have the following measures:

Question

m<B = 25 degrees
m<C= (3x)degrees
and m<D = (3x+5) degrees.
What are the measures of <C and <D?

Answer 1

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.