Together, the measures of ∠B
, ∠C
, and ∠D
equal 180°
. The angles have the following measures: m∠B=25°
, m∠C=(3x)°
, and m∠D=(3x+5)°
. What are the measures of ∠C
and ∠D
?(1 point)
m∠C=
°
m∠D=
°
We are given that the sum of the measures of ∠B, ∠C, and ∠D is 180°. So we can write an equation:
m∠B + m∠C + m∠D = 180
Substituting in the given values:
25 + 3x + (3x + 5) = 180
Combine like terms:
25 + 6x + 5 = 180
Combine constant terms:
30 + 6x = 180
We want to isolate the variable term, so we subtract 30 from both sides:
6x = 180 - 30
6x = 150
Now we divide both sides by 6 to solve for x:
x = 150/6
x = 25
Now that we know the value of x, we can find the measures of ∠C and ∠D:
m∠C = 3x = 3(25) = 75°
m∠D = 3x + 5 = 3(25) + 5 = 75 + 5 = 80°
So the measures of ∠C and ∠D are:
m∠C = 75°
m∠D = 80°