The image shows a triangle with angle measures indicated in terms of $x$. Specifically:

• $\angle A = 4x - 10$
• $\angle B = x$
• $\angle C = x + 16$

To find the measure of $\angle A$, we will use the fact that the sum of the interior angles of a triangle is always 180 degrees. Therefore, the equation is:

$(4x - 10) + x + (x + 16) = 180$

Let me solve this equation step by step.

1. Combine like terms: $6x + 6 = 180$

2. Subtract 6 from both sides: $6x = 174$

3. Divide by 6: $x = 29$

Now that we know $x = 29$, we can substitute this value back into the expression for $\angle A$:

$\angle A = 4x - 10 = 4(29) - 10 = 116 - 10 = 106^\circ$

Thus, the measure of $\angle A$ is $106^\circ$.

Would you like further explanation or details?

Related Questions:

1. How can you find the measures of $\angle B$ and $\angle C$?
2. Why does the sum of the angles in a triangle always equal 180 degrees?
3. What types of triangles exist based on angle measures?
4. How would the equation change if the triangle was not a right triangle?
5. Can you classify this triangle based on the given angle measures?

Tip:

Always check the sum of your angle measures when working with triangles to ensure they add up to 180°.