To find the measure of angle $A$, we first analyze the given information.

Step 1: Set Up the Equation

The three angles in the triangle are given as:

• Angle $A = x$
• Angle $B = 5x$
• Angle $C = 3x$

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

$x + 5x + 3x = 180$

Step 2: Solve for $x$

Combine like terms:

$9x = 180$

Now, divide both sides by 9:

$x = 20$

Step 3: Find the Measure of Angle $A$

Since $A = x$, we substitute $x = 20$:

$A = 20^\circ$

Answer

The measure of angle $A$ is $20^\circ$.

Would you like further details or have any questions?

Here are 5 related questions to expand on this topic:

1. What would the measures of angles $B$ and $C$ be?
2. How do you determine if a triangle is valid based on its angles?
3. What are the properties of an isosceles triangle, and does this triangle fit those properties?
4. How can we classify this triangle based on its angles (acute, right, obtuse)?
5. How would the angle measures change if the equation had a different total sum?

Tip: Always verify your results by checking if the calculated angle measures add up to $180^\circ$ in a triangle.