Two angles, ∠1
and ∠2
, in a diagram are complementary. If m∠2=26° , what equation can you write to solve for m∠1
Since two angles are complementary, it means that the sum of their measures is 90 degrees. Therefore, the equation to solve for m∠1 would be:
m∠1 + m∠2 = 90°
Substituting the given measure of m∠2:
m∠1 + 26° = 90°
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
To find the measures of ∠C and ∠D, we need to write an equation based on the given information.
According to the problem, the sum of the measures of ∠B, ∠C, and ∠D is equal to 180°.
Therefore, we can write the equation as:
m∠B + m∠C + m∠D = 180°
Substituting the given measures:
25° + 3x° + (3x + 5)° = 180°
Combine like terms:
25° + 3x° + 3x° + 5° = 180°
6x° + 30° = 180°
Subtract 30° from both sides of the equation:
6x° = 150°
Divide both sides of the equation by 6:
x = 25°
Now, substitute the value of x back into the measures of ∠C and ∠D:
m∠C = 3x° = 3(25°) = 75°
m∠D = 3x° + 5° = 3(25°) + 5° = 75° + 5° = 80°
Therefore, the measures of ∠C and ∠D are 75° and 80°, respectively.