In $$ riangle A B C, \mathrm{~m} \angle A=(2 x+6)^{\circ}, \mathrm{m} \angle B=(5 x-2)^{\circ} $$, and $$ \mathrm{m} \angle C=(3 x+6)^{\circ} $$. Find $$ \mathrm{m} \angle B $$.

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In $$ 	riangle A B C, \mathrm{~m} \angle A=(2 x+6)^{\circ}, \mathrm{m} \angle B=(5 x-2)^{\circ} $$, and $$ \mathrm{m} \angle C=(3 x+6)^{\circ} $$. Find $$ \mathrm{m} \angle B $$.

UpStudy AI · Accepted Answer

1. Since $$ \triangle ABC $$ is a triangle, the sum of its interior angles is $$ 180^\circ $$:
   $$
   (2x+6)^\circ + (5x-2)^\circ + (3x+6)^\circ = 180^\circ.
   $$

2. Combine like terms:
   $$
   2x + 5x + 3x + 6 - 2 + 6 = 180.
   $$
   This simplifies to:
   $$
   10x + 10 = 180.
   $$

3. Solve for $$ x $$:
   $$
   10x = 180 - 10 = 170,
   $$
   $$
   x = \frac{170}{10} = 17.
   $$

4. Substitute $$ x = 17 $$ into the expression for $$ \mathrm{m} \angle B $$:
   $$
   \mathrm{m} \angle B = (5x - 2)^\circ = 5(17) - 2 = 85 - 2 = 83^\circ.
   $$

Thus, $$ \mathrm{m} \angle B $$ is $$ 83^\circ $$.
$$ \mathrm{m} \angle B = 83^\circ $$.

In \( \triangle A B C, \mathrm{~m} \angle A=(2 x+6)^{\circ}, \mathrm{m} \angle B=(5 x-2)^{\circ} \), and \( \mathrm{m} \angle C=(3 x+6)^{\circ} \). Find \( \mathrm{m} \angle B \).

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