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?(1 point)
m∠C=
°

m∠D=
°

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Answer 1

To find the measures of ∠C and ∠D, we can set up an equation and solve for x.

Since the sum of the angles ∠B, ∠C, and ∠D is equal to 180°, we have:

25° + (3x)° + (3x + 5)° = 180°.

Combining like terms, we get:

25° + 6x + 5° = 180°.

Simplifying the equation further, we have:

6x + 30° = 180°.

Subtracting 30° from both sides, we have:

6x = 150°.

Dividing both sides by 6, we find:

x = 25°.

Now that we have the value of x, we can substitute it back into the expressions for ∠C and ∠D:

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°.