Together, the measures B,C,D equal 180 degrees. The angles have the following measures: m<B=25, M<C=(3x), M<D= (3x+5). What are the measures of C and D?
Given that the sum of angles B, C, and D equals 180 degrees, we can write the equation:
25 + 3x + 3x + 5 = 180
Combine like terms:
25 + 6x + 5 = 180
30 + 6x = 180
Subtract 30 from both sides:
6x = 150
Divide by 6:
x = 25
Now, substitute x back into the expressions for angles C and D:
C = 3x = 3(25) = 75
D = 3x + 5 = 3(25) + 5 = 75 + 5 = 80
Therefore, the measure of angle C is 75 degrees and the measure of angle D is 80 degrees.
I’m the diagram, M<A=(4x-10) and M<D=((2x+22). What is the measure of D
Given that the sum of angles in a triangle is 180 degrees, we can write the equation:
(4x - 10) + A + (2x + 22) = 180
Combine like terms:
4x - 10 + A + 2x + 22 = 180
6x + 12 + A = 180
Now, we are given that angle A measures 25 degrees, so we can substitute that into the equation:
6x + 12 + 25 = 180
6x + 37 = 180
Subtract 37 from both sides:
6x = 143
Divide by 6:
x = 23.83
Now, substitute x back into the expression for angle D:
D = 2x + 22 = 2(23.83) + 22 ≈ 69.67 + 22 ≈ 91.67
Therefore, the measure of angle D is approximately 91.67 degrees.