Points D, E, and F are the midpoints of sides \overline{BC}, \overline{CA}, and \overline{AB} of \triangle ABC, respectively, and \overline{CZ} is an altitude of the triangle. If \angle BAC = 71^\circ, \angle ABC = 39^\circ, and \angle BCA = 70^\circ, then what is \angle EZD+\angle EFD in degrees?
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angle EFD is 70
To find the sum of angles EZD and EFD, we need to determine the measure of each angle individually.
Let's start by finding the measure of angle EZD. Since D is the midpoint of side BC, angle EZD is opposite angle ABC. Therefore, we need to find the measure of angle ABC.
In triangle ABC, we are given that angle BAC = 71°, angle ABC = 39°, and angle BCA = 70°.
To find angle ABC, we can use the fact that the sum of the three angles in any triangle is 180°.
So, angle ABC = 180° - (angle BAC + angle BCA)
= 180° - (71° + 70°)
= 180° - 141°
= 39°
Now that we know that angle ABC is 39°, we can determine the measure of angle EZD by simply recognizing that angle EZD is equal to angle ABC.
Therefore, angle EZD = 39°.
Next, let's find the measure of angle EFD. F is the midpoint of side AB, so angle EFD is opposite angle BCA.
Since we already know that angle BCA is 70°, angle EFD will also be equal to 70°.
Now we can find the sum of angles EZD and EFD.
Sum of angles EZD + EFD = angle EZD + angle EFD
= 39° + 70°
= 109°
Therefore, the sum of angles EZD and EFD is 109°.