Questions: Unit 3 Homework 2 If (m angle 3=54^circ), find the measure of each (angle 1= square angle 2= square angle 4= square angle 11= square angle 12= square)

Transcript text: Unit 3 Homework 2 If $m \angle 3=54^{\circ}$, find the measure of ea \[ \begin{array}{l} \angle 1=\square \angle 2=\square \quad \angle 4=\square \\ \angle 11=\square \angle 12=\square \end{array} \]

Solution

Solution Steps

Step 1: Identify the given angle

The problem states that $ m\angle 3 = 54^\circ $.

Step 2: Determine the measure of vertical angles

Vertical angles are equal. Therefore, $ m\angle 3 = m\angle 7 $. So, $ m\angle 7 = 54^\circ $.

Step 3: Determine the measure of corresponding angles

Corresponding angles are equal. Since $ m\angle 3 = 54^\circ $, the corresponding angle to $ \angle 3 $ is $ \angle 11 $. Therefore, $ m\angle 11 = 54^\circ $.

Final Answer

$ m\angle 1 = 126^\circ $ (since $ \angle 1 $ and $ \angle 3 $ are supplementary)
$ m\angle 2 = 54^\circ $ (since $ \angle 2 $ and $ \angle 3 $ are alternate interior angles)
$ m\angle 4 = 126^\circ $ (since $ \angle 4 $ and $ \angle 3 $ are supplementary)
$ m\angle 11 = 54^\circ $ (corresponding angle to $ \angle 3 $)
$ m\angle 12 = 126^\circ $ (since $ \angle 12 $ and $ \angle 11 $ are supplementary)
$ m\angle 13 = 54^\circ $ (since $ \angle 13 $ and $ \angle 12 $ are alternate interior angles)

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