Questions: Lines A and B are parallel. Find the measure of angle a.

Transcript text: Lines $A$ and $B$ are parallel. Find the measure of $\angle a$.

Solution

Solution Steps

Step 1: Identify the given angle

The given angle is 47°. This angle is formed by line A and the transversal.

Step 2: Identify the relationship between the given angle and angle _a_

Angle _a_ and the given angle (47°) are consecutive interior angles. Consecutive interior angles are supplementary when the lines are parallel.

Step 3: Calculate the measure of angle _a_

Since the lines A and B are parallel, the sum of consecutive interior angles is 180°. Therefore, the measure of angle _a_ can be found by subtracting the given angle from 180°:

$a = 180° - 47°$ $a = 133°$

Final Answer

\$\boxed{133^\circ}\$

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