Question

question 10 (5 points)
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find ( mangle boc ) in the figure if ( mangle aoc = 77^{circ} ).
a) ( 18^{circ} )
b) ( 59^{circ} )
c) ( 65^{circ} )
d) ( 71^{circ} )

Explanation:

Step1: Set up the angle equation

From the figure, we know that \( \angle AOC=\angle AOB + \angle BOC \). Given \( \angle AOB = 3x \) and \( \angle BOC=7x + 17 \), and \( m\angle AOC = 77^{\circ} \). So we can set up the equation: \( 3x+(7x + 17)=77 \).

Step2: Solve for x

Simplify the left - hand side of the equation: \( 3x+7x + 17=10x + 17 \). Then we have the equation \( 10x+17 = 77 \). Subtract 17 from both sides: \( 10x=77 - 17=60 \). Divide both sides by 10: \( x=\frac{60}{10}=6 \).

Step3: Calculate \( m\angle BOC \)

Since \( \angle BOC = 7x + 17 \), substitute \( x = 6 \) into the expression: \( 7\times6+17=42 + 17=59^{\circ} \).

Answer:

B) \( 59^{\circ} \)