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 + 15) . What are the measures of <C and <D
We know that the sum of the measures of angles B, C, and D is 180. This can be expressed as:
m<B + m<C + m<D = 180
Substituting the given measures:
25 + 3x + 3x + 15 = 180
Combine like terms:
6x + 40 = 180
Subtract 40 from both sides:
6x = 140
Divide both sides by 6:
x = 23.33
Substituting this value back into the expressions for m<C and m<D:
m<C = 3x = 3 * 23.33 = 69.99
m<D = 3x + 15 = 3 * 23.33 + 15 = 69.99 + 15 = 84.99
Therefore, the measures of <C and <D are approximately 69.99° and 84.99°, respectively.
wrong
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We know that the sum of the measures of angles B, C, and D is 180 degrees. This can be expressed as:
m<B + m<C + m<D = 180
Substituting the given measures:
25 + 3x + (3x + 15) = 180
Combine like terms:
25 + 6x + 15 = 180
40 + 6x = 180
Subtract 40 from both sides:
6x = 140
Divide both sides by 6:
x = 23.33
Substituting this value back into the expressions for m<C and m<D:
m<C = 3x = 3 * 23.33 = 69.99
m<D = 3x + 15 = 3 * 23.33 + 15 = 69.99 + 15 = 84.99
Therefore, the measures of angle C and angle D are approximately 69.99° and 84.99°, respectively.