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Sagot :
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].
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].
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