Let's solve the problem step-by-step to find the measure of the third angle in the triangle.
1. Understand the problem:
We are given two angles of a triangle: [tex]\( 28^\circ \)[/tex] and [tex]\( 93^\circ \)[/tex]. We need to find the measure of the third angle. Note that the sum of the angles in any triangle is always [tex]\( 180^\circ \)[/tex].
2. Calculate the sum of the given angles:
Add the measures of the two given angles:
[tex]\[
28^\circ + 93^\circ = 121^\circ
\][/tex]
3. Determine the measure of the third angle:
Subtract the sum of the given angles from the total [tex]\( 180^\circ \)[/tex] to find the measure of the third angle:
[tex]\[
180^\circ - 121^\circ = 59^\circ
\][/tex]
4. Compare with the given options:
The given options are:
- [tex]\( 59^\circ \)[/tex]
- [tex]\( 87^\circ \)[/tex]
- [tex]\( 121^\circ \)[/tex]
- [tex]\( 152^\circ \)[/tex]
From this comparison, we see that the third angle measures [tex]\( 59^\circ \)[/tex].
Therefore, the measure of the third angle in the triangle is [tex]\( 59^\circ \)[/tex], which matches the first option given. The correct answer is [tex]\( 59^\circ \)[/tex].
