https://file.aiquickdraw.com/mathbot/file/1728530714009gcdjylfp.jpg

The image shows a triangle with two known angles: 65° and 105°, and two unknown angles labeled \(g\) and \(h\). The sum of the interior angles of a triangle always equals 180°. Using this, we can find the missing angle \(g\) as follows:

\[
g + 65^\circ + 105^\circ = 180^\circ
\]
\[
g + 170^\circ = 180^\circ
\]
\[
g = 180^\circ - 170^\circ = 10^\circ
\]

Now, let's look at the exterior angle at vertex \(g\). This exterior angle is given as 105°, which means that angle \(h\) is supplementary to it (since exterior and interior angles at the same vertex sum to 180°):

\[
h + 105^\circ = 180^\circ
\]
\[
h = 180^\circ - 105^\circ = 75^\circ
\]

Thus, the missing angles are:
- \( g = 10^\circ \)
- \( h = 75^\circ \)

Would you like more details or have any further questions?

Here are some related questions to explore:
1. How do we know that the sum of angles in a triangle is always 180°?
2. Can you explain how exterior and interior angles are related?
3. What is the general method for solving for unknown angles in polygons?
4. How would you apply the angle sum rule to polygons with more than three sides?
5. What are other properties of triangles, like the different types of triangles based on angles?

**Tip:** Remember that exterior angles are always equal to the sum of the two non-adjacent interior angles!

Find the missing angles of the triangle with given angles of 65° and 105°.

Learn how to find the missing angles of a triangle with known angles of 65° and 105°. This step-by-step solution explains the Angle Sum Theorem and the concept of supplementary angles. Suitable for students in Grades 7-9.

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