https://file.aiquickdraw.com/mathbot/file/1726725659521dnz1rjhq.jpg

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?

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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.

If m∠ADC = 79°, m∠BDC = (2x + 10)°, and m∠ADB = (4x - 15)°, find the degree measure of ∠BDC and ∠ADB. The diagram is not to scale.

In this problem, you will learn how to find the degree measures of ∠BDC and ∠ADB using algebra and the angle sum property of a straight line. The problem involves setting up an equation using given expressions for angles, solving for x, and calculating the unknown angles. This solution is ideal for students in Grades 8-10.

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