Together, the measures of ∠B , ∠C , and ∠D equal 180°

Question

. 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 ?

Answer 1

Let's use the information given and set up an equation to solve for x.

According to the problem, the sum of the measures of angles B, C, and D is 180°.

m∠B + m∠C + m∠D = 180°

Substituting the given values:

25° + (3x)° + (3x + 5)° = 180°

Combining like terms:

25° + 3x° + 3x° + 5° = 180°

Simplifying the equation:

6x + 30° = 180°

Subtracting 30° from both sides:

6x = 150°

Dividing both sides by 6:

x = 25°

Now that we have found the value of x, we can substitute it back into the expressions for ∠C and ∠D to find their measures.

m∠C = (3x)° = 3(25°) = 75°

m∠D = (3x + 5)° = 3(25°) + 5° = 75° + 5° = 80°

Therefore, the measure of ∠C is 75° and the measure of ∠D is 80°.