Triangle Angle Relationships - Pre Algebra

1. The angles of a triangle are in the ratio $2 : 3 : 4$. What are their measures?

   $40^\circ$, $60^\circ$ and $80^\circ$. The 9 parts share $180^\circ$, so each part is $20^\circ$.

2. An exterior angle of a triangle measures $130^\circ$. What is the adjacent interior angle?

   $50^\circ$. They form a linear pair, so they add to $180^\circ$.

3. How are the base angles of an isosceles triangle related?

   They are congruent. They are the angles opposite the two equal sides.

4. The angles of a triangle measure $x^\circ$, $2x^\circ$ and $3x^\circ$. What is $x$?

   $x = 30$, since $6x = 180$.

5. The vertex angle of an isosceles triangle is $40^\circ$. What is each base angle?

   $70^\circ$. The base angles share $180 - 40 = 140$ degrees equally.

6. The two remote interior angles of a triangle measure $40^\circ$ and $75^\circ$. What is the exterior angle?

   $115^\circ$, the sum of the remote interior angles.

7. What is the sum of the interior angles of any triangle?

   $180^\circ$.

8. What is the measure of each angle of an equilateral triangle?

   $60^\circ$, since three equal angles add to $180^\circ$.

9. Two angles of a triangle measure $50^\circ$ and $65^\circ$. What is the third angle?

   $65^\circ$, since $180 - 50 - 65 = 65$.

10. What is the sum of the exterior angles of a triangle, taking one at each vertex?

    $360^\circ$.

11. What does the exterior angle theorem say about a triangle?

    An exterior angle equals the sum of the two interior angles that are not adjacent to it (the remote interior angles).

12. One acute angle of a right triangle measures $35^\circ$. What is the other acute angle?

    $55^\circ$. The acute angles of a right triangle add to $90^\circ$.

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