Question

which statements about the diagram are true? select three options.

\\(x = 63\\)
\\(y = 47\\)
\\(z = 117\\)
\\(x + y = 180\\)
\\(x + z = 180\\)

Explanation:

Identify vertical angles

Using the Vertical Angles Theorem knowledge point

$$ x = 63 $$

Find angle y

Using the Alternate Interior Angles Theorem knowledge point

$$ y = 47 $$

Find angle z

Using the linear pair relationship

$$ z + 63 = 180 \implies z = 117 $$

Verify sum relationships

Using the calculated values

$$ x + y = 63 + 47 = 110 e 180 $$

$$ x + z = 63 + 117 = 180 $$

Answer:

• (A) \(x = 63\) (Correct answer)
• (B) \(y = 47\)
• (C) \(z = 117\) (Correct answer)
• (D) \(x + y = 180\)
• (E) \(x + z = 180\) (Correct answer)