To solve this problem, we use the triangle angle sum property, which states that the sum of the angles in a triangle is always $180^\circ$.

Given:

• First angle = $61^\circ$
• Second angle = $84^\circ$

Let the third angle be $x$. According to the triangle angle sum property:

$61^\circ + 84^\circ + x = 180^\circ$

Simplifying:

$145^\circ + x = 180^\circ$

Subtracting $145^\circ$ from both sides:

$x = 180^\circ - 145^\circ = 35^\circ$

Thus, the measure of the third angle is $35^\circ$.

Would you like a detailed explanation or further assistance?

Here are 5 related questions to explore:

1. What is the triangle angle sum property?
2. How do you calculate missing angles in a triangle?
3. What are the properties of an obtuse triangle?
4. Can a triangle have more than one obtuse angle?
5. How can the triangle inequality theorem help determine side lengths?

Tip: Always check if the sum of the given angles equals $180^\circ$ to verify calculations!