Two angles,∠1 and ∠2, in a diagram are complementary. If m∠2 = 26°, what equation can you write to solve for m∠1? (1 point)
Since the angles are complementary, the sum of their measures is 90°. Therefore, we can write the equation:
m∠1 + m∠2 = 90°.
From this equation, we can solve for m∠1 by substituting the given value m∠2 = 26°:
m∠1 + 26° = 90°.
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 ?
Since ∠3 and ∠5 are vertical angles, they have the same measure. Therefore, we can write:
m∠3 = m∠5.
Since ∠4 and ∠5 are supplementary angles, the sum of their measures is 180°. Therefore, we can write:
m∠4 + m∠5 = 180°.
Given that m∠3 = 67°, we can substitute this value into the first equation:
67° = m∠5.
Substituting this value into the second equation, we can write:
m∠4 + 67° = 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 ?
Since the sum of the measures of ∠B, ∠C, and ∠D equals 180°, we can write the equation:
m∠B + m∠C + m∠D = 180°
Substituting the given measures of ∠B = 25°, ∠C = (3x)°, and ∠D = (3x + 5)°, we have:
25° + (3x)° + (3x + 5)° = 180°
Simplifying and combining like terms, we get:
6x + 30 = 180
Subtracting 30 from both sides, we have:
6x = 150
Dividing both sides by 6, we get:
x = 25
Substituting the value of x back into the measures of ∠C and ∠D, we have:
∠C = (3x)° = (3 * 25)° = 75°
∠D = (3x + 5)° = (3 * 25 + 5)° = 80°
Therefore, the measure of ∠C is 75° and the measure of ∠D is 80°.