Question

question 13 (1 point) what is the measure of ∠cad? diagram with points a, b, c, d, angles 85°, 70° options: a) 15 degrees, b) 70 degrees, c) 85 degrees. question 14 (1 point) what is the measure of ∠dac? diagram with points e, d, c, d, angles 65°, 40°, 45° options: a) 40 degrees, b) 45 degrees, c) 65 degrees.

Explanation:

Question 13

Step1: Analyze angle relationships

From the diagram, we know that the sum of \(\angle CAD\), \(85^\circ\), and \(70^\circ\) should relate to a right angle or a straight angle? Wait, actually, looking at the angles around point \(A\), the angle between \(AB\) and the other ray (let's see, the angle marked \(85^\circ\) and \(70^\circ\), so to find \(\angle CAD\), we can use the fact that \(85^\circ=\angle CAD + 70^\circ\)? Wait, no, maybe the total angle from \(AB\) to the ray with \(C\) is \(85^\circ\), and from \(AB\) to the ray with \(D\) is \(85^\circ+\angle CAD\)? Wait, no, let's re - examine. The angle between \(AB\) and \(AC\) is \(70^\circ\), and the angle between \(AB\) and \(AD\) is \(85^\circ\). So \(\angle CAD=\angle BAD-\angle BAC\). Here, \(\angle BAD = 85^\circ\) and \(\angle BAC = 70^\circ\).

Step2: Calculate \(\angle CAD\)

\(\angle CAD=85^{\circ}-70^{\circ}\)
\(\angle CAD = 15^{\circ}\)

From the diagram (assuming the angle marked \(45^\circ\) is \(\angle DAC\)), we can directly see that the measure of \(\angle DAC\) is \(45^\circ\).

Answer:

A) 15 degrees

Question 14

(Note: There seems to be a typo in the diagram label, but assuming the angles around the vertex are \(65^\circ\), \(40^\circ\), and \(45^\circ\) and we need to find \(\angle DAC\). Wait, maybe the straight line or a right angle? Wait, if we assume that the sum of angles on one side of a straight line is \(180^\circ\), but maybe it's a different case. Wait, looking at the options, if we consider that maybe the angle \(\angle DAC\) is given as \(45^\circ\) from the diagram (since one of the angles is marked \(45^\circ\) near \(D\) and \(C\)). Wait, maybe the diagram shows that \(\angle DAC = 45^\circ\).