Math / Geometry

QuestionIn the figure below, $m \angle 2=126^{\circ}$ . Find $m \angle 1, m \angle 3$ , and $m \angle 4$ .

Studdy Solution

STEP 1

1. Vertically opposite angles are equal.
2. The sum of angles on a straight line is $180^\circ$ .

STEP 2

1. Identify the relationship between angles.
2. Calculate $m \angle 1$ .
3. Calculate $m \angle 3$ .
4. Calculate $m \angle 4$ .

STEP 3

Identify that angles 1 and 3 are vertically opposite, and angles 2 and 4 are vertically opposite. Therefore, $m \angle 1 = m \angle 3$ and $m \angle 2 = m \angle 4$ .

STEP 4

Since angles 1 and 2 are on a straight line, their sum is $180^\circ$ . Therefore, we have:
$m \angle 1 + m \angle 2 = 180^\circ$
Substitute $m \angle 2 = 126^\circ$ :
$m \angle 1 + 126^\circ = 180^\circ$

STEP 5

Solve for $m \angle 1$ :
$m \angle 1 = 180^\circ - 126^\circ$ $m \angle 1 = 54^\circ$

STEP 6

Since $m \angle 1 = m \angle 3$ (vertically opposite angles), we have:
$m \angle 3 = 54^\circ$

STEP 7

Since $m \angle 2 = m \angle 4$ (vertically opposite angles), we have:
$m \angle 4 = 126^\circ$
The measures of the angles are: $m \angle 1 = 54^\circ$ $m \angle 3 = 54^\circ$ $m \angle 4 = 126^\circ$

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