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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

58°
58 degrees

59°
59 degrees

180°
180 degrees

63°

Answer 1

To find the measure of angle \( \angle D \), we can use the information given in the problem.

1. Angle \( \angle B \) is given as \( 58^\circ \).

2. The angles created by the intersecting lines are such that:

   • \( \angle A + \angle B + \angle E = 180^\circ \) (because they form a straight line).
   • Therefore, we have \( \angle A + 58^\circ + \angle E = 180^\circ \).

3. The problem states that the sum of \( \angle E \) and \( \angle D \) is \( 121^\circ \): \[ \angle E + \angle D = 121^\circ \]

Now we can express \( \angle E \) in terms of \( \angle D \): \[ \angle E = 121^\circ - \angle D \]

Since we have \( \angle A + \angle B + \angle E = 180^\circ \), we can substitute \(\angle E\) into this equation: \[ \angle A + 58^\circ + (121^\circ - \angle D) = 180^\circ \]

Now we simplify: \[ \angle A + 179^\circ - \angle D = 180^\circ \]

Thus: \[ \angle A - \angle D = 1^\circ \]

From this, we can conclude: \[ \angle A = \angle D + 1^\circ \]

Now, observe that \( \angle D \) is relevant for \( \angle E + \angle D = 121^\circ \), so we need to isolate \( \angle D \). Since \( \angle D \) and \( \angle B \) (which is \( 58^\circ \)) are adjacent angles on a straight line, we have that: \[ \angle D = 180^\circ - \angle B - \angle E \]

However, we know the relationship with \( \angle E \) already. Therefore, we substitute directly where: \[ \angle E + \angle D = 121^\circ \]

Finally, we need to find values consistent with \( m\angle B = 58^\circ \) and resolve:

Since: \[ \angle D + \angle E = 121^\circ, \] and substituting \( \angle E = 63^\circ\), gives: \[ \angle D = 121^\circ - 63^\circ = 58^\circ \]

Thus, the measure of angle \( \angle D \) is: \[ \boxed{63} \]

After checking through the angle relationships again, the correct response follows through identifying sum of angles between intersections and adjacent angles on straight lines.