Question

puzzle #3 1 if m∠b = 9x + 15° and m∠c = 3x - 3°, what is the value of x? 2 find m∠b 3 find m∠c find m∠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 angle - sum property

Assume angles A, B and C are in a triangle and their sum is 180°. But since we are not given information about angle A yet and we can use the fact that angles B and C are supplementary (as they form a linear - pair, 180°). So \(m\angle B+m\angle C = 180^{\circ}\). Substitute the given expressions: \((9x + 15)+(3x-3)=180\).

Step2: Simplify the left - hand side

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 the expression for \(m\angle B\): \(m\angle B=9x + 15=9\times14+15=126 + 15=141\).

Step5: Find \(m\angle C\)

Substitute \(x = 14\) into the expression for \(m\angle C\): \(m\angle C=3x-3=3\times14-3=42 - 3=39\).

Step6: Find \(m\angle A\)

Since \(m\angle B\) and \(m\angle A\) are supplementary (linear - pair), \(m\angle A=180 - m\angle B=180 - 141 = 39\).

Answer:

1. D. 14
2. C. 141
3. A. 39
4. A. 39