https://file.aiquickdraw.com/mathbot/file/1730159357690z4vhpq69.jpg

In the image, we are given a triangle \( \triangle ABC \) with the following angle measures:

- \( m \angle A = 8x \)
- \( m \angle B = 10x \)
- \( m \angle C = 7x + 5 \)

Since the sum of the angles in a triangle is always \( 180^\circ \), we can set up the following equation:

\[
8x + 10x + (7x + 5) = 180
\]

Simplifying, we get:

\[
25x + 5 = 180
\]

Subtracting 5 from both sides:

\[
25x = 175
\]

Dividing both sides by 25:

\[
x = 7
\]

Now, substitute \( x = 7 \) back into the expression for \( m \angle A \):

\[
m \angle A = 8x = 8 \times 7 = 56
\]

Thus, the measure of \( \angle A \) is \( 56^\circ \).

**Answer:** The correct choice is **56**.

Would you like more details, or do you have any questions?

Here are five related questions:
1. How can we verify if a triangle is valid using its angles?
2. What would be the measures of \( \angle B \) and \( \angle C \) in this triangle?
3. How would the solution change if the sum of angles in a polygon other than a triangle was used?
4. What are the conditions for solving unknowns in triangles with algebra?
5. Can you use trigonometric functions to determine side lengths given these angle measures?

**Tip:** Always check that the sum of calculated angles adds up to 180 degrees for a triangle, ensuring accuracy in your solution.

Find the measure of the indicated angle \( m \angle A \) in \( \triangle ABC \) with \( m \angle A = 8x \), \( m \angle B = 10x \), and \( m \angle C = 7x + 5 \).

Learn how to find the measure of angle A in a triangle with given algebraic expressions for each angle. This solution uses the Triangle Angle Sum Theorem and basic algebraic equations, suitable for Grade 8 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation