Finding Unknown Angles Around a Point

Q1. Determine the values of $a$, $b$, and $c$ given the angles around a point: $110^ ext{o}$, $a^ ext{o}$, $b^ ext{o}$, $65^ ext{o}$, $c^ ext{o}$, $20^ ext{o}$.

Background

Topic: Geometry – Angles Around a Point

This question tests your understanding of the geometric property that the sum of all angles around a point is $360^ ext{o}$. You are asked to solve for the unknown angles $a$, $b$, and $c$ using this property.

Key Terms and Formulas

• Angle around a point: The sum of all angles formed at a single point is $360^ ext{o}$.

• Equation:

$110 + a + b + 65 + c + 20 = 360$

Step-by-Step Guidance

1. Write the equation for the sum of all angles around the point: $110 + a + b + 65 + c + 20 = 360$.

2. Combine the known angle values: $110 + 65 + 20 = 195$.

3. Rewrite the equation with the combined known angles: $195 + a + b + c = 360$.

4. Isolate the unknowns by subtracting the sum of the known angles from $360$:$a + b + c = 360 - 195$.

Try solving on your own before revealing the answer!

Final Answer: $a + b + c = 165$

Each unknown angle can be found if additional information is given or if the diagram provides relationships (such as equal angles or supplementary angles). Here, the sum of $a$, $b$, and $c$ is $165^ ext{o}$.

We used the property that the sum of angles around a point is $360^ ext{o}$ and subtracted the known angles to find the sum of the unknowns.