Question

Question

Use the image to answer the question.

An upward line intersects with another upward line, creating angles upper A degrees and upper B degrees in the upper left and right angles of the intersection, and upper E degrees in the lower left of the intersection. Another ray extends downward to the right from the point of intersection, and creates angles upper C degrees to the right of the ray and upper D degrees to the left of the ray.

If m∠B=58°
, and the sum of m∠E
and m∠D
is 121°
, what is the measure of ∠D
?

(1 point)
Responses

180°
180 degrees

63°
63 degrees

59°
59 degrees

58°

Answer 1

To solve for the measure of ∠D, we start by analyzing the information given.

1. We know that m∠B = 58°.
2. The sum of m∠E and m∠D is given as 121°: \[ m∠E + m∠D = 121° \]

Since m∠B and m∠E are vertically opposite angles, they are equal. Therefore: \[ m∠E = m∠B = 58° \]

Now, we can substitute m∠E into the equation to find m∠D: \[ 58° + m∠D = 121° \]

To find m∠D, we can rearrange this equation: \[ m∠D = 121° - 58° \] \[ m∠D = 63° \]

Thus, the measure of ∠D is: \[ \boxed{63} \]

So the correct response is 63 degrees.