In a diagram, ∠3 and ∠5 are vertical angles, and ∠4 is a supplementary angle with ∠5. If m∠3=67°, what equation can you write to solve for m∠4?(1 point) m∠4+°=°
The equation that can be written to solve for m∠4 is:
m∠3 + m∠4 = 180°
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)
To find the measures of ∠C and ∠D, we can set up the equation:
m∠B + m∠C + m∠D = 180°
Substituting the given measures, we have:
25° + 3x + (3x + 5)° = 180°
Combining like terms, we get:
6x + 30° = 180°
Subtracting 30° from both sides, we have:
6x = 150°
Dividing by 6, we get:
x = 25°
Now we can find the measures of ∠C and ∠D by substituting x back into the expressions:
m∠C = 3x = 3(25°) = 75°
m∠D = 3x + 5 = 3(25°) + 5 = 75° + 5° = 80°
Therefore, ∠C measures 75° and ∠D measures 80°.