Let's solve the missing angles using the property of triangles that the sum of all internal angles in a triangle is always $180^\circ$. For each question, we will calculate the missing angle $x^\circ$.

1.

Given angles: $79^\circ$ and $82^\circ$. $x^\circ = 180^\circ - (79^\circ + 82^\circ) = 180^\circ - 161^\circ = 19^\circ$

2.

Given angles: $68^\circ$ and $49^\circ$. $x^\circ = 180^\circ - (68^\circ + 49^\circ) = 180^\circ - 117^\circ = 63^\circ$

3.

Given angles: $53^\circ$ and $90^\circ$ (right angle). $x^\circ = 180^\circ - (53^\circ + 90^\circ) = 180^\circ - 143^\circ = 37^\circ$

4.

Given angles: $34^\circ$ and $27^\circ$. $x^\circ = 180^\circ - (34^\circ + 27^\circ) = 180^\circ - 61^\circ = 119^\circ$

5.

Given angles: $53^\circ$ and $58^\circ$. $x^\circ = 180^\circ - (53^\circ + 58^\circ) = 180^\circ - 111^\circ = 69^\circ$

6.

Given angles: $90^\circ$ (right angle) and $19^\circ$. $x^\circ = 180^\circ - (90^\circ + 19^\circ) = 180^\circ - 109^\circ = 71^\circ$

Would you like further explanations on any of these steps? Here are some related questions:

1. What is the sum of the interior angles of a triangle?
2. How do you solve for a missing angle in a right triangle?
3. Can a triangle have more than one right angle?
4. How does the sum of angles in other polygons compare to triangles?
5. What are the different types of triangles based on angles?

Tip: When working with angles in a triangle, always remember the sum is $180^\circ$. This rule applies to all types of triangles!