Question

puzzle #3
1 if ( mangle b = 9x + 15^{circ}) and ( mangle c = 3x - 3^{circ}), what is the value of ( x)?
2 find ( mangle b)
3 find ( mangle c)
4 find ( mangle a)
answer choices
a: 39 b: 48 c: 141
d: 14 e: 12 f: 19
g: 72 h: 156 i: 3
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Explanation:

Step1: Use the property of supplementary angles

Since \(\angle B\) and \(\angle C\) are supplementary (\(\angle B+\angle C = 180^{\circ}\)), we substitute the expressions for \(\angle B\) and \(\angle C\).
\((9x + 15)+(3x-3)=180\)

Step2: Simplify the left - hand side of the equation

Combine like terms: \(9x+3x+15 - 3=180\), which gives \(12x+12 = 180\)

Step3: Solve for \(x\)

Subtract \(12\) from both sides: \(12x=180 - 12=168\). Then divide both sides by \(12\): \(x=\frac{168}{12}=14\)

Step4: Find \(m\angle B\)

Substitute \(x = 14\) into \(m\angle B=9x + 15\). So \(m\angle B=9\times14+15=126 + 15=141\)

Step5: Find \(m\angle C\)

Substitute \(x = 14\) into \(m\angle C=3x-3\). So \(m\angle C=3\times14-3=42 - 3=39\)

Step6: Find \(m\angle A\)

Since \(\angle A\) and \(\angle C\) are vertical angles (vertical angles are equal), \(m\angle A=m\angle C = 39\)

Answer:

DCAI