Question

solve for x. show all your work.
① 117° 56°
② 34° 126°

Explanation:

Step1: Use angle - sum property of a triangle and parallel - line properties for part (a)

The angle supplementary to $117^{\circ}$ is $180 - 117=63^{\circ}$. The angle corresponding to the $56^{\circ}$ angle (due to parallel lines) and the $63^{\circ}$ angle and $x$ are angles of a triangle. By the angle - sum property of a triangle ($\text{sum of angles in a triangle}=180^{\circ}$), we have $x + 63+56 = 180$.

Step2: Solve the equation for $x$ in part (a)

$x=180-(63 + 56)=180 - 119 = 61^{\circ}$.

Step3: Use angle - sum property of a triangle and parallel - line properties for part (b)

The angle supplementary to $126^{\circ}$ is $180 - 126 = 54^{\circ}$. The angle corresponding to the $34^{\circ}$ angle (due to parallel lines) and the $54^{\circ}$ angle and $x$ are angles of a triangle. By the angle - sum property of a triangle ($\text{sum of angles in a triangle}=180^{\circ}$), we have $x+34 + 54=180$.

Step4: Solve the equation for $x$ in part (b)

$x=180-(34 + 54)=180 - 88 = 92^{\circ}$.

Answer:

a. $x = 61^{\circ}$
b. $x = 92^{\circ}$