Question

quiz (2.6, 3.1 - 3.3) in the figure below, the measure of ∠1 = 3x°, the measure of ∠2 = y°, and the measure of ∠3 = 78°. find the value of each variable. x = (type a whole number.) y = (type a whole number.) this quiz: 12 point(s) possible this question: 1 point(s) possible 12 of 12

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. $\angle1$ and $\angle3$ are vertical angles, so $3x = 78$.

Step2: Solve for $x$

Divide both sides of the equation $3x = 78$ by 3. $x=\frac{78}{3}=26$.

Step3: Use linear - pair property

$\angle2$ and $\angle3$ form a linear - pair, so $\angle2+\angle3 = 180^{\circ}$. Since $\angle3 = 78^{\circ}$, then $y + 78=180$.

Step4: Solve for $y$

Subtract 78 from both sides of the equation $y + 78=180$. $y=180 - 78=102$.

Answer:

$x = 26$
$y = 102$