which statements about the diagram are true? select three options. \n□x = 63\n□y = 47\n□z = 117\n□x + y =…
which statements about the diagram are true? select three options. \n□x = 63\n□y = 47\n□z = 117\n□x + y = 180\n□x + z = 180
Answer
Explanation:
Step1: Use vertical - angle property
Vertical angles are equal. The angle with measure $x^{\circ}$ and the $63^{\circ}$ angle are vertical angles, so $x = 63$.
Step2: Use vertical - angle property
The angle with measure $y^{\circ}$ and the $47^{\circ}$ angle are vertical angles, so $y = 47$.
Step3: Use the property of supplementary angles
The angle with measure $z^{\circ}$ and the $63^{\circ}$ angle are supplementary (linear - pair), so $z=180 - 63=117$.
Step4: Check the sum of angles
$x + y=63 + 47 = 110\neq180$. $x+z = 63+117=180$.
Answer:
$x = 63$, $y = 47$, $x + z = 180$