Question

find the measure of the missing angles.
answer attempt 2 out of 2
b = \boxed{\space}^\circ \quad c = \boxed{\space}^\circ

Explanation:

Step1: Find angle \( b \)

Angle \( b \) and the \( 36^\circ \) angle are supplementary (they form a linear pair), so their sum is \( 180^\circ \).
\( b + 36^\circ = 180^\circ \)
\( b = 180^\circ - 36^\circ = 144^\circ \)

Step2: Find angle \( c \)

Angle \( c \) and the \( 36^\circ \) angle are vertical angles (or angle \( c \) and angle \( b \) are supplementary). Vertical angles are equal, or using linear pair with \( b \):
\( c + b = 180^\circ \) (linear pair), so \( c = 180^\circ - 144^\circ = 36^\circ \). Alternatively, vertical angles with \( 36^\circ \) give \( c = 36^\circ \).

Answer:

\( b = \boxed{144}^\circ \)
\( c = \boxed{36}^\circ \)