To solve for the measure of ∠A, we need to use the triangle's angle sum property. Here's how we can approach this:

Given:

• ∠A = $8x$
• ∠B = $10x$
• ∠C = $7x + 5$

Since the sum of the angles in any triangle is 180°, we can write the equation: $8x + 10x + (7x + 5) = 180$ Simplifying the equation: $25x + 5 = 180$ $25x = 175$ $x = \frac{175}{25} = 7$

Plugging back the value of $x = 7$ into ∠A:

$∠A = 8x = 8(7) = 56°$

Therefore, the measure of ∠A is 56°.

Would you like more details or have any questions?

Here are five related questions:

1. How would you calculate the measure of ∠B and ∠C after solving for $x$?
2. What is the general formula for the sum of angles in any polygon?
3. Could this method be applied to non-triangular polygons, and how would it differ?
4. How can you verify if your result is correct after solving for the angles?
5. What role does the exterior angle property play in such triangle problems?

Tip: Always check if the sum of the calculated angles equals 180° to verify the accuracy of your solution!