To determine the measure of one of the angles of Triangle A, given that it is similar to Triangle B, we first need to know the measures of all the angles in Triangle B.
1. Identify Given Angles of Triangle B:
Triangle B has two given angles:
[tex]\[
\angle B_1 = 30^\circ
\][/tex]
[tex]\[
\angle B_2 = 70^\circ
\][/tex]
2. Calculate the Third Angle of Triangle B:
The sum of the interior angles in any triangle is always [tex]\(180^\circ\)[/tex]. Therefore, we can find the third angle [tex]\(\angle B_3\)[/tex] using the following equation:
[tex]\[
\angle B_3 = 180^\circ - (\angle B_1 + \angle B_2)
\][/tex]
Substitute the known values:
[tex]\[
\angle B_3 = 180^\circ - (30^\circ + 70^\circ)
\][/tex]
Simplify the calculation:
[tex]\[
\angle B_3 = 180^\circ - 100^\circ
\][/tex]
[tex]\[
\angle B_3 = 80^\circ
\][/tex]
3. List the Angles of Triangle B:
Now we know all three angles of Triangle B:
[tex]\[
\angle B_1 = 30^\circ
\][/tex]
[tex]\[
\angle B_2 = 70^\circ
\][/tex]
[tex]\[
\angle B_3 = 80^\circ
\][/tex]
4. Determine the Similarity of Triangle A:
Since Triangle A is similar to Triangle B, it means that Triangle A has the same set of angles as Triangle B. Therefore, Triangle A's angles must be:
[tex]\[
30^\circ, 70^\circ, \text{ and } 80^\circ
\][/tex]
5. Choose the Correct Answer:
Given the answer choices are [tex]\(20^\circ, 40^\circ, 60^\circ, \text{ and } 80^\circ\)[/tex], the angle that matches one of Triangle B's angles (also Triangle A's angles) is:
[tex]\[
80^\circ
\][/tex]
Thus, the measure of one of the angles of Triangle A is:
[tex]\[
\boxed{80^\circ}
\][/tex]
