Examine the diagram.

A triangle has angles A, 60 degrees, 55 degrees. A line is at the top of the triangle and forms angles B, C, and 65 degrees. Angle C is opposite to angle with measure 60 degrees.

The diagram shows parallel lines cut by two transversal lines creating a triangle. Which statement can be made from the diagram?
mAngleB + mAngleC + 55° = 180°
mAngleA + 60° + 55° = 180°
mAngleC = 55°
mAngleA = 55°

1 answer

To analyze the triangle and the angles involved based on the description you provided, let's summarize the information:

  1. You have a triangle with angles A, 60°, and 55°.
  2. There is also a line that creates angles B, C, and 65°.
  3. Angle C is opposite the 60° angle in the triangle.

Using the properties of triangles and the fact that the sum of angles in any triangle is 180°, we can examine the options:

  1. mAngleB + mAngleC + 55° = 180°: This is a possible statement if you consider that the angles B, C, and the 55° angle are angles in a triangle that totals 180°. However, we need to know what angle C is to confirm if this equation is appropriate.

  2. mAngleA + 60° + 55° = 180°: This statement can be confirmed as true because the angles A, 60°, and 55° are the angles of the triangle, and they do indeed add up to 180°.

  3. mAngleC = 55°: Based on your description, this statement looks to be incorrect. Angle C, as you said, is opposite the 60° angle, which suggests that angle C cannot be 55°.

  4. mAngleA = 55°: This statement can be true according to the information given. If angle A is the one measuring 55°, that would also fit with the previously mentioned angle configuration in the triangle.

Considering this analysis, the strongest statement that can be made from the diagram is:

mAngleA + 60° + 55° = 180°.

That captures the fundamental angle-sum property in a triangle correctly.