Question

calculate the measure of ∠b. circle your answer.

Explanation:

Step1: Identify angle relationship

The angle \( \angle b \) and the \( 39^\circ \) angle are supplementary (they form a linear pair, so their sum is \( 180^\circ \)).

Step2: Calculate \( \angle b \)

Using the supplementary angle formula: \( \angle b + 39^\circ = 180^\circ \). Solving for \( \angle b \), we get \( \angle b = 180^\circ - 39^\circ \).
\( \angle b = 141^\circ \) (Wait, but the handwritten note has \( 6 = 282 \), maybe there's a different diagram? Wait, looking at the left diagram, maybe there are two \( 39^\circ \) angles and we need to find the reflex angle? Wait, the total around a point is \( 360^\circ \). If there are two \( 39^\circ \) angles, then \( \angle b = 360^\circ - 39^\circ - 39^\circ \). Let's recalculate.

Step1 (corrected): Total angle around a point

The sum of angles around a point is \( 360^\circ \). There are two \( 39^\circ \) angles and \( \angle b \).

Step2 (corrected): Calculate \( \angle b \)

\( \angle b = 360^\circ - 39^\circ - 39^\circ \)
\( \angle b = 360 - 78 \)
\( \angle b = 282^\circ \) (matches the handwritten note)

Answer:

\( 282^\circ \)