Answer:
Hence, we have measure of angle 2 to be 15°. (i.e. m∠2=15°)
Step-by-step explanation:
We will use the property that:
Alternate interior angles have the same measure.
As we know that 'angle 1 ' and 50° are alternate interior angles hence they must be equal.
Hence, m∠1=50°
Also we now that sum of all the angles of a triangle is equal to 180°.
Hence,
m∠2+m∠1+115°=180°
⇒ m∠2+50°+115°=180°
⇒ m∠2+165°=180°
⇒ m∠2=180°-165°
⇒ m∠2=15°
Hence, m∠2=15°.
The measure of angle 2 (∠2) of the given parallelogram is; C: 15°
From the diagram of the parallelogram given, we see that;
∠1 and 50° are alternate interior angles and according to angle theorems, they are equal.
Thus;
∠1 = 50°
Now, to find ∠2, we know that sum of angles in a triangle is 180°
Thus;
50° + 115° + ∠2 = 180°
∠2 = 180° - (50° + 115°)
∠2 = 180° - 165°
∠2 = 15°
Read more about alternate Interior angles at; https://brainly.com/question/24839702
