Question

9 multiple - choice 2 points which is a correct statement about vertical angles? vertical angles are always supplementary. vertical angles are always congruent. vertical angles are always acute. vertical angles are always complementary. 10 multiple - choice 2 points what is the measure of the largest angle in the accompanying triangle? (2x + 1) (x + 15) x 46.5 83 56 41

Explanation:

Step1: Recall vertical - angle property

Vertical angles are formed by two intersecting lines and are always congruent. They are not always supplementary (sum to 180°), complementary (sum to 90°), or acute (less than 90°). So for question 9, the correct statement is that vertical angles are always congruent.

Step2: Use angle - sum property of a triangle for question 10

The sum of the interior angles of a triangle is 180°. So, \((2x + 1)+(x + 15)+x=180\).
First, combine like - terms: \(2x+1+x + 15+x=180\), which simplifies to \(4x+16 = 180\).
Then, subtract 16 from both sides: \(4x=180 - 16=164\).
Next, divide both sides by 4: \(x=\frac{164}{4}=41\).
The angles are:
\(2x + 1=2\times41+1=82 + 1=83\).
\(x + 15=41+15=56\).
\(x = 41\).
The largest angle is 83°.

Answer:

1. Vertical angles are always congruent.
2. 83