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: Find the value of \(x\)

Since \(x\) and \(63^{\circ}\) are vertical angles, \(x = 63\).

Step2: Find the value of \(z\)

Since \(z\) and \(63^{\circ}\) are supplementary angles (\(z+63 = 180\)), \(z=180 - 63=117\).

Step3: Find the value of \(y\)

Using the angle - sum property of a triangle (the sum of angles in a triangle is \(180^{\circ}\)), if one angle is \(47^{\circ}\), another is \(63^{\circ}\), then \(y=180-(47 + 63)=70\).

Step4: Check \(x + y\) and \(x+z\)

\(x + y=63 + 70=133
eq180\).
\(x+z=63 + 117 = 180\).

Answer:

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