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

Answer 1

If the measures of ∠B, ∠C, and ∠D add up to 180°, we can write the following equation:

∠B + ∠C + ∠D = 180°

Substituting the given measures, we get:

25° + 3x° + (3x+5)° = 180°

Simplifying the equation, we combine like terms:

25° + 6x° + 5° = 180°

30° + 6x° = 180°

Next, we isolate the variable by subtracting 30° from both sides:

6x° = 150°

Finally, we solve for x by dividing both sides by 6:

x = 25

Now, we can substitute the value of x back into the measures of ∠C and ∠D:

∠C = 3x° = 3(25)° = 75°

∠D = 3x+5° = 3(25)+5° = 80°

Therefore, the measures of ∠C and ∠D are 75° and 80°, respectively.