Question

in the figure below, $m\angle 1 = (x - 9)\degree$ and $m\angle 2 = 6x\degree$. find the angle measures. $m\angle 1 = \square\degree$ $m\angle 2 = \square\degree$

Explanation:

Step1: Recognize supplementary angles

$\angle 1$ and $\angle 2$ form a straight line, so they are supplementary: $m\angle 1 + m\angle 2 = 180^\circ$

Step2: Substitute given expressions

$(x-9) + 6x = 180$

Step3: Simplify and solve for $x$

$7x - 9 = 180$
$7x = 189$
$x = 27$

Step4: Calculate $m\angle 1$

$m\angle 1 = (27 - 9)^\circ = 18^\circ$

Step5: Calculate $m\angle 2$

$m\angle 2 = 6\times27^\circ = 162^\circ$

Answer:

$m\angle 1 = 18^\circ$
$m\angle 2 = 162^\circ$