if m∠8 = 45°, what equation can you write to find the value of m∠7?
Since the measures of angles 7 and 8 are supplementary, meaning they add up to 180 degrees, the equation that can be written is:
m∠7 + m∠8 = 180°
Substituting the given value for m∠8, the equation becomes:
m∠7 + 45° = 180°
Together, the measures of ∠B, ∠C and ∠D equal 180 degrees. The angles have the following measures: m∠B = 25 degrees, m∠C = (3x) degrees, and m∠D = (3x + 5) degrees. What are the measures of ∠C and ∠D?
Given that ∠B, ∠C, and ∠D add up to 180 degrees, the equation can be written as:
m∠B + m∠C + m∠D = 180°
Substituting the given measures, the equation becomes:
25° + 3x° + (3x + 5)° = 180°
Combining like terms, the equation simplifies to:
25° + 6x + 5° = 180°
Combining constants, the equation further simplifies to:
6x + 30° = 180°
Subtracting 30° from both sides of the equation, we get:
6x = 150°
Dividing both sides of the equation by 6, we find:
x = 25°
Substituting x back into the measures of ∠C and ∠D, we find:
m∠C = 3(25°) = 75°
m∠D = 3(25°) + 5° = 80°
Therefore, the measure of ∠C is 75 degrees and the measure of ∠D is 80 degrees.