Let's solve problem 5 step by step.

The problem states:

• $m\angle ADC = 79^\circ$,
• $m\angle BDC = (2x + 10)^\circ$,
• $m\angle ADB = (4x - 15)^\circ$.

We are asked to find the degree measures of $\angle BDC$ and $\angle ADB$.

Approach:

1. Use the angle sum property of a straight line: Since $\angle ADC$ is a straight angle and the sum of angles on a straight line is 180°, we can write the equation:

   $m\angle ADC = m\angle ADB + m\angle BDC$

   Substituting the given expressions:

   $79^\circ = (4x - 15)^\circ + (2x + 10)^\circ$

2. Solve for $x$:

   Combine like terms:

   $79^\circ = 6x - 5^\circ$

   Add $5^\circ$ to both sides:

   $84^\circ = 6x$

   Divide both sides by 6:

   $x = 14^\circ$

3. Find the measures of $\angle BDC$ and $\angle ADB$:

   • $m\angle BDC = 2x + 10 = 2(14) + 10 = 28 + 10 = 38^\circ$
   • $m\angle ADB = 4x - 15 = 4(14) - 15 = 56 - 15 = 41^\circ$

Final answer:

• $m\angle BDC = 38^\circ$
• $m\angle ADB = 41^\circ$

Would you like a deeper explanation of the steps, or do you have any questions?

Here are 5 related questions you might find helpful:

1. What is the sum of angles on a straight line?
2. How do you solve for unknowns in linear equations?
3. What is the angle sum property of a triangle?
4. How can you verify your solution in a geometry problem?
5. How do angles on intersecting lines relate to each other?

Tip: When solving geometry problems, it's essential to carefully set up equations based on known properties like the sum of angles on a straight line or within a triangle.