Question

in the figure, $m\angle 1 = (5x)\degree$ and $m\angle 2 = (x + 18)\degree$.
(a) write an equation to find $x$. make sure you use an \=\ sign in your answer.
equation:
(b) find the degree measure of each angle.
$m\angle 1 = \square\degree$
$m\angle 2 = \square\degree$

Explanation:

Part (a)

Step1: Identify angle relationship

Angles 1 and 2 form a linear pair, so their sum is \(180^\circ\).

Step2: Write the equation

Given \(m\angle1 = (5x)^\circ\) and \(m\angle2=(x + 18)^\circ\), the equation is \(5x+(x + 18)=180\). Simplify to \(5x+x + 18=180\) or \(6x+18 = 180\). But the form with the two angle expressions equal to 180 (since they are supplementary) is \(5x+(x + 18)=180\) (or simplified as \(6x+18=180\)). However, if we consider the two angles adding to 180, the equation can be written as \(5x+(x + 18)=180\) (or \(5x+x + 18 = 180\) or \(6x+18=180\)). But the most direct from the angle measures is \(5x+(x + 18)=180\).

Step1: Solve the equation for \(x\)

Start with the equation from part (a), say \(6x+18 = 180\). Subtract 18 from both sides: \(6x=180 - 18=162\). Then divide by 6: \(x=\frac{162}{6}=27\).

Step2: Find \(m\angle1\)

Substitute \(x = 27\) into \(m\angle1=5x\). So \(m\angle1=5\times27 = 135\).

Step3: Find \(m\angle2\)

Substitute \(x = 27\) into \(m\angle2=x + 18\). So \(m\angle2=27+18 = 45\).

Answer:

\(5x+(x + 18)=180\) (or equivalent like \(6x + 18=180\))

Part (b)