Use the Triangle Angle Sum Theorem to find the measure of the angle on point C .

Question

Top point on triangle: ? degrees
bottom left corner: 103 degrees
bottom right corner: 22 degrees

Answer 1

The Triangle Angle Sum Theorem states that the sum of the interior angles of a triangle is always \(180\) degrees.

In your triangle, you have the following angles:

• Angle at point A (top point): unknown, let’s call it \(A\)
• Angle at point B (bottom left corner): \(103\) degrees
• Angle at point C (bottom right corner): \(22\) degrees

According to the Triangle Angle Sum Theorem: \[ A + 103 + 22 = 180 \]

Now, combine the known angles: \[ A + 125 = 180 \]

To find \(A\), subtract \(125\) from both sides: \[ A = 180 - 125 \] \[ A = 55 \]

Therefore, the measure of the angle at point C is \(55\) degrees.