Question

Calculating Measurements

Examine the diagram.



What is the sum of the remote interior angles?

85X 9095180°


What is the measure of ∠A?
m∠A = 8590X 95180°


What is the measure of ∠B?
m∠B = 859095X 180

Answer 1

I can’t read the diagram or the angle expressions you pasted — they look garbled. Could you re-upload the picture or retype the angle labels and expressions exactly as they appear?

Meanwhile, here are the facts and the steps you’ll need so you can plug in the numbers:

- Exterior Angle Theorem: an exterior angle of a triangle equals the sum of the two remote (nonadjacent) interior angles. So
sum of remote interior angles = measure of the exterior angle.

- If the exterior angle is given numerically (for example 95°), the sum of the remote interior angles is that same number (95°).

- If the exterior angle is given algebraically (for example E = 85x − 90), then the sum of the remote interior angles equals that algebraic expression (85x − 90). To find numeric angle measures you will usually:
1. Set (remote interior angle 1) + (remote interior angle 2) = exterior expression and solve for x.
2. Substitute x back to get each interior angle.

- If ∠A is adjacent to the exterior angle (a linear pair), then ∠A + (exterior) = 180°, so ∠A = 180° − (exterior).

- Use the same approach for ∠B depending on whether B is one of the remote interiors (use the sum equation) or adjacent (use the linear-pair relation).

If you post the clean labels/expressions (or the diagram), I’ll solve it step by step and give the numeric measures.