Question

in the figure, $m\angle 1 = (x + 78)\degree$ and $m\angle 2 = (2x)\degree$.
(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

\( (x + 78) + 2x = 180 \)

Step1: Solve for \(x\)

Combine like terms: \(3x + 78 = 180\)
Subtract 78: \(3x = 180 - 78 = 102\)
Divide by 3: \(x = \frac{102}{3} = 34\)

Step2: Find \(m\angle 1\)

Substitute \(x = 34\) into \(m\angle 1 = (x + 78)^\circ\):
\(m\angle 1 = 34 + 78 = 112^\circ\)

Step3: Find \(m\angle 2\)

Substitute \(x = 34\) into \(m\angle 2 = (2x)^\circ\):
\(m\angle 2 = 2 \times 34 = 68^\circ\)

Answer:

\(x + 78 + 2x = 180\)

Part (b)