Question

use the image below to find the requested values. find the measure of ∠mkd.

Explanation:

Step1: Assume angle - sum property

Let's assume that \(\angle MKD+\angle DKB = 180^{\circ}\) (linear - pair of angles) or we need more information. If we assume that \(\angle MKD\) and \(\angle DKB\) are adjacent angles and the information is complete as it is, and we know that \(\angle DKB = 54^{\circ}\) and \(\angle MKD=2r + 20\). But if we assume that the two non - overlapping angles \(\angle MKD\) and \(\angle DKB\) form a straight - line at point \(K\), then \(\angle MKD+\angle DKB = 180^{\circ}\). So, \(2r + 20+54=180\).

Step2: Solve for \(r\)

First, simplify the left - hand side of the equation: \(2r+74 = 180\). Then subtract 74 from both sides: \(2r=180 - 74\), so \(2r = 106\). Divide both sides by 2: \(r = 53\).

Step3: Find \(\angle MKD\)

Substitute \(r = 53\) into the expression for \(\angle MKD\). \(\angle MKD=2r + 20\). So, \(\angle MKD=2\times53+20\). \(2\times53 = 106\), then \(106+20=126^{\circ}\).

Answer:

\(126^{\circ}\)