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) find ( mangle a)
answer choices
a: 39 b: 48 c: 141
d: 14 e: 12 f: 19
g: 72 h: 156 i: 3
type the 4 - letter code into the answer box. all caps, no spaces.

Explanation:

Step1: Use supplementary angles relationship

Angles \(B\) and \(C\) are supplementary (\(m\angle B + m\angle C=180^{\circ}\)).
Substitute \(m\angle B = 9x + 15^{\circ}\) and \(m\angle C=3x - 3^{\circ}\) into the equation: \((9x + 15)+(3x - 3)=180\).
Simplify the left - hand side: \(9x+15 + 3x-3=12x + 12\).
So, \(12x+12 = 180\).

Step2: Solve for \(x\)

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

Step3: Find \(m\angle B\)

Substitute \(x = 14\) into \(m\angle B=9x + 15\).
\(m\angle B=9\times14+15=126 + 15=141^{\circ}\).

Step4: Find \(m\angle C\)

Substitute \(x = 14\) into \(m\angle C=3x - 3\).
\(m\angle C=3\times14-3=42 - 3=39^{\circ}\).

Step5: Find \(m\angle A\)

Since \(m\angle A=m\angle C\) (vertical angles), \(m\angle A = 39^{\circ}\).

Answer:

D, C, A, A