Question

puzzle #5
1 if m∠a = 3x - 10° and m∠c = x + 16°, what is the value of x?
answer choices
a: 13 b: 61 c: 105
d: 136 e: 43 f: 39
g: 29 h: 151 i: 47
2 find m∠a
3 find m∠d
4 find m∠b
type the 4 - letter code into the answer box. all caps, no spaces.
agh
keep trying! you can do it!
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Explanation:

Step1: Assume vertical - angle relationship

Since vertical angles are equal, assume $\angle A$ and $\angle C$ are vertical angles, so $m\angle A=m\angle C$. Then we have the equation $3x - 10=x + 16$.

Step2: Solve the equation for x

Subtract x from both sides: $3x-x-10=x - x+16$, which simplifies to $2x-10 = 16$. Then add 10 to both sides: $2x-10 + 10=16 + 10$, getting $2x=26$. Divide both sides by 2: $x = 13$.

Step3: Find $m\angle A$

Substitute $x = 13$ into the expression for $m\angle A$: $m\angle A=3x-10=3\times13 - 10=39 - 10=29$.

Step4: Find $m\angle D$

Assume the angles are part of a right - angled intersection situation. If $\angle A$ and $\angle D$ are complementary (since the intersection seems to have a right - angle), and $m\angle A = 29^{\circ}$, then $m\angle D=90 - 29 = 61$.

Step5: Find $m\angle B$

If $\angle A$ and $\angle B$ are supplementary (a straight - line pair), then $m\angle B=180 - 29=151$.

Answer:

13, 29, 61, 151 (corresponding to the values of x, $m\angle A$, $m\angle D$, $m\angle B$ respectively) and the 4 - letter code is AGHB.