Question

which statements about the diagram are true? select three options.
□x = 63
□y = 47
□z = 117
□x + y = 180
□x + z = 180

Explanation:

Step1: Use vertical angles and linear - pair relationships

Vertical angles are equal. A linear pair of angles sums to \(180^{\circ}\).
We know that \(x = 63\) (vertical angles).
Since \(z\) and \(63^{\circ}\) form a linear pair, \(z+63 = 180\), so \(z=180 - 63=117\).
For \(y\), using the triangle - angle - sum property (the sum of angles in a triangle is \(180^{\circ}\)) is not necessary here. But if we consider the parallel - line and transversal properties (alternate interior angles etc. is not the case here). However, if we use the fact that \(x + z=63 + 117=180\) (linear pair)

Step2: Check each option

• For \(x = 63\): True (vertical angles).
• For \(y = 47\): False.
• For \(z = 117\): True (\(z+63 = 180\)).
• For \(x + y=180\): False.
• For \(x + z=180\): True (\(63+117 = 180\))

Answer:

\(x = 63\), \(z = 117\), \(x + z=180\)