Question

19 use the angle addition postulate to find m∠cdy, if m∠cde = 122° and m∠yde = 86° diagram a 63° b 208° c 36° d 58°

Explanation:

Step1: Recall Angle Addition Postulate

The Angle Addition Postulate states that if a point \( Y \) lies in the interior of \( \angle CDE \), then \( m\angle CDE = m\angle CDY + m\angle YDE \). We can rearrange this formula to solve for \( m\angle CDY \): \( m\angle CDY = m\angle CDE - m\angle YDE \).

Step2: Substitute the given values

We know that \( m\angle CDE = 122^\circ \) and \( m\angle YDE = 86^\circ \). Substituting these values into the formula from Step 1, we get:
\( m\angle CDY = 122^\circ - 86^\circ \)

Step3: Calculate the result

Performing the subtraction: \( 122 - 86 = 36 \), so \( m\angle CDY = 36^\circ \). Wait, but let's check the diagram again. Wait, maybe I misread the angles. Wait, looking at the diagram, \( \angle YDE \) – wait, maybe the angle between \( DY \) and \( DE \) is 90 degrees? Wait, no, the problem says \( m\angle CDE = 122^\circ \) and \( m\angle YDE = 86^\circ \). Wait, no, maybe the diagram has \( DE \) vertical, \( DY \) horizontal left, and \( DC \) below \( DY \). Wait, maybe the Angle Addition Postulate is \( m\angle CDE = m\angle CDY + m\angle YDE \), but if \( \angle YDE \) is actually the angle between \( DY \) and \( DE \), which is 90 degrees? Wait, no, the problem states \( m\angle YDE = 86^\circ \). Wait, maybe I made a mistake. Wait, let's recalculate: \( 122 - 86 = 36 \), but option C is 36? Wait, the options are A. 63, B. 208, C. 36, D. 58? Wait, no, maybe the diagram is different. Wait, maybe \( \angle CDE = 122^\circ \), \( \angle YDE = 86^\circ \), so \( \angle CDY = \angle CDE - \angle YDE = 122 - 86 = 36^\circ \). So the answer should be C. 36°? Wait, but let me check again. Wait, maybe the angle between \( DY \) and \( DE \) is 90 degrees, but the problem says 86. So according to the problem, the calculation is 122 - 86 = 36. So the correct option is C. 36°.

Answer:

C. \( 36^\circ \)