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the sum of a triangle always equals 180 degrees

To determine whether a given set of angles can be the measures of a triangle, the sum of the three angles must equal 180° because the sum of interior angles of a triangle is always 180°.

Let's check each set of angles:

### (a) \( 70^\circ, 70^\circ, 40^\circ \)
\[
70 + 70 + 40 = 180^\circ
\]
These angles **can** be the measures of a triangle.

### (b) \( 95^\circ, 45^\circ, 25^\circ \)
\[
95 + 45 + 25 = 165^\circ
\]
These angles **cannot** be the measures of a triangle, since their sum is not 180°.

### (c) \( 35^\circ, 21^\circ, 124^\circ \)
\[
35 + 21 + 124 = 180^\circ
\]
These angles **can** be the measures of a triangle.

### (d) \( 54^\circ, 59^\circ, 67^\circ \)
\[
54 + 59 + 67 = 180^\circ
\]
These angles **can** be the measures of a triangle.

### Summary:
- (a) Can be angle measures of a triangle.
- (b) Cannot be angle measures of a triangle.
- (c) Can be angle measures of a triangle.
- (d) Can be angle measures of a triangle.

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the exterior angle theorem for triangles?
2. Can a triangle have two 90° angles?
3. How do angle measures relate to the type of triangle (acute, obtuse, right)?
4. What happens if one angle in a triangle is greater than 180°?
5. Can there be a triangle where all angles are less than 60°?

**Tip:** When solving angle problems in geometry, always double-check the sum of interior angles to confirm if a valid triangle is possible.

For each set of three measures, determine if they can be angle measures of a triangle: (a) 70°, 70°, 40°; (b) 95°, 45°, 25°; (c) 35°, 21°, 124°; (d) 54°, 59°, 67°.

Determine if sets of three given angles, including 70°, 70°, 40° and 95°, 45°, 25°, can be measures of a triangle. Learn about the Triangle Angle Sum Theorem and how to verify if angle measures are valid for forming a triangle.

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