Question

ABCD is a parallelogram with diagonal AC. If the measure of angle CAB is 21° and the measure of angle ADC is 125°, what is the measure of angle DAC?

Answer 1

Answer:  The measure of angle DAC is 44°.

Step-by-step explanation:  As shown in the attached figure below, ABCD is a parallelogram with diagonal AC, where

$m\angle CAB=21^\circ,~~~m\angle ADC=125^\circ.$

We are to find the measure of angle DAC.

Let x° be the measure of angle DAC.

We know that

if two parallel lines are cut by a transversal, then the sum of the interior angles on one side of the transversal is 180°.

In parallelogram ABCD, AB is parallel to CD and DA is a transversal, so the sum of the measures of the interior angles ADC and BAD is 180°.

Therefore,

$m\angle ADC+m\angle BAD=180^\circ\\\\ \Rightarrow 125^\circ+m\angle CAB+m\angle DAC=180^\circ\\\\\Rightarrow 125^\circ+21^\circ+x^\circ=180^\circ\\\\\Rightarrow 136^\circ+x^\circ=180^\circ\\\\\Rightarrow x^\circ=180^\circ-136^\circ\\\\\Rightarrow x^\circ=44^\circ.$

Thus, the measure of angle DAC is 44°.

Answer 2

Answer:

∠CAD is 34°

Step-by-step explanation:

Given:

ABCD is a parallelogram

AC is diagonal of the parallelogram.

∠CAB = 21°  and ∠ADC = 125°

To find: ∠DAC

We know that sum of the interior angle on the same side of the traversal is 180°.

So,

∠BAD + ∠ADC = 180

∠CAB + ∠CAD + 125 = 180

21 + ∠CAD = 180 - 125

∠CAD = 55 - 21

∠CAD = 34

Therefore, ∠CAD is 34°