The angles in the given diagram are determined as follows: ACE is 115 degrees due to alternate interior angles, DCB is 35 degrees, and ACB is 30 degrees within triangle ABC.
Let us start by calculating the measure of angle ACE:
Since AB and CD are parallel to each other, this makes angles BAC and ACE equal as they are alternate interior angles.
Thus, the angle ACE will also be equal to 115 degrees.
Now we will calculate the angle DCB:
For this, we can observe the diagram and see that angles ABC and DCB are also alternate interior angles. Therefore the measure of angle DCB is also 35 degrees.
Now we will calculate the value of angle ACB:
In triangle ABC, angle A is 115 and angle B is 35 degrees.
Therefore, the angle ACB will be 180-115+35= 30 degrees.
The complete question is:
In this diagram, lines AB and CD are parallel.
Angle ABC measures 35° and angle BAC measures 115°.
What are the measures of the following angles?
1. m∠ACE = ___°
2. m∠DCB = ___°
3. m∠ACB = ___ °