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) m∠C=° m∠D=°
We know that the sum of the measures of angles in a triangle is 180°.
Therefore, we can set up the equation: ∠B + ∠C + ∠D = 180°.
Substituting the given measures, we have:
25° + 3x° + (3x+5)° = 180°.
Simplifying the equation, we get:
25° + 6x° + 5° = 180°.
Combining like terms, we have:
30° + 6x° = 180°.
Now, we can solve for x:
6x° = 150°.
Dividing both sides of the equation by 6, we get:
x = 25°.
Now that we have the value of x, we can find the measures of ∠C and ∠D:
m∠C = 3x° = 3(25°) = 75°.
m∠D = (3x+5)° = (3(25°)+5°) = 80°.
Therefore, the measures of ∠C and ∠D are:
m∠C = 75°.
m∠D = 80°.
In the diagram, m∠A=(4x−10)° and m∠D=(2x+22)° . What is the measure of ∠D ? (1 point) °
We know that the sum of the measures of angles in a quadrilateral is 360°.
Therefore, we can set up the equation: ∠A + ∠D = 360°.
Substituting the given measures, we have:
(4x - 10)° + (2x + 22)° = 360°.
Combining like terms, we have:
6x + 12° = 360°.
Now, we can solve for x:
6x = 348°.
Dividing both sides of the equation by 6, we get:
x = 58°.
Now that we have the value of x, we can find the measure of ∠D:
m∠D = (2x + 22)° = (2(58°) + 22°) = 138°.
Therefore, the measure of ∠D is 138°.
There are two complementary angles, ∠5 and ∠6. If m∠5=39°, what equation can you write to solve for m∠6?(1 point) Responses m∠6+39°=90° x plus 39 degrees equals 90 degrees m∠6+39°=180° x plus 39 degrees equals 180 degrees m∠6=39° x equals 39 degrees m∠6=180°−39° x equals 180 degrees minus 39 degrees
Since ∠5 and ∠6 are complementary angles, their measures add up to 90°.
Therefore, the equation to solve for m∠6 is:
m∠6 + 39° = 90°.
Two angles, ∠1 and ∠2 , in a diagram are supplementary. If m∠1=77°, what equation can you write to solve for m∠2? Let m∠2=x° (1 point) Responses x°=77° x equals 77 degrees x°+77°=90° x plus 77 degrees equals 90 degrees x°=90°−77° x equals 90 degrees minus 77 degrees x°+77°=180°
Since ∠1 and ∠2 are supplementary angles, their measures add up to 180°.
Therefore, the equation to solve for m∠2 is:
m∠2 + 77° = 180°.
that is not an answer
Apologies for the confusion, here is the correct equation:
m∠2 + 77° = 180°.