To solve for the measure of the third angle in a triangle where the other two angles are given, we need to use the fundamental property of triangles: the sum of the interior angles of any triangle is always [tex]\( 180^\circ \)[/tex].
Given:
- First angle, [tex]\( \angle1 = 102^\circ \)[/tex]
- Second angle, [tex]\( \angle2 = 67^\circ \)[/tex]
Step-by-step solution:
1. Add the measures of the two given angles:
[tex]\[
\angle1 + \angle2 = 102^\circ + 67^\circ
\][/tex]
2. Calculate the sum:
[tex]\[
102^\circ + 67^\circ = 169^\circ
\][/tex]
3. Subtract this sum from the total measure of the interior angles of a triangle, [tex]\( 180^\circ \)[/tex]:
[tex]\[
\text{Third angle} = 180^\circ - 169^\circ
\][/tex]
4. Perform the subtraction:
[tex]\[
180^\circ - 169^\circ = 11^\circ
\][/tex]
Therefore, the measure of the third angle is [tex]\( 11^\circ \)[/tex].
So, the correct answer is [tex]\( 11^\circ \)[/tex].
