Let's solve each question based on the information provided in the images.

First Question:

Given:

• $m\angle A = 35^\circ$
• $m\angle C = 79^\circ$

We need to find $m\angle B$.

In any triangle, the sum of the interior angles is $180^\circ$. So, $m\angle A + m\angle B + m\angle C = 180^\circ$ Substitute the known values: $35^\circ + m\angle B + 79^\circ = 180^\circ$ Simplify: $m\angle B = 180^\circ - 35^\circ - 79^\circ$ $m\angle B = 180^\circ - 114^\circ = 66^\circ$ Thus, $m\angle B = 66^\circ$.

Second Question:

Given:

• $m\angle B = 35^\circ$
• $m\angle C = 64^\circ$

We need to find $m\angle A$.

Using the same formula for the sum of angles in a triangle: $m\angle A + m\angle B + m\angle C = 180^\circ$ Substitute the known values: $m\angle A + 35^\circ + 64^\circ = 180^\circ$ Simplify: $m\angle A = 180^\circ - 35^\circ - 64^\circ$ $m\angle A = 180^\circ - 99^\circ = 81^\circ$ Thus, $m\angle A = 81^\circ$.

Let me know if you'd like further explanation on these solutions or have any additional questions!

Here are some related questions to explore further:

1. How would you find the missing angle if all three angles in a triangle are unknown?
2. What would happen if the triangle were an isosceles or equilateral triangle?
3. How can you verify your answer for an angle in a triangle problem?
4. How does the exterior angle theorem help in finding angles in triangles?
5. What are the properties of the different types of triangles (acute, obtuse, right) based on angle measures?

Tip: In any triangle problem, start by checking if you have enough information to apply the angle sum property, which states that the interior angles always sum to 180 degrees.