Given $$ P B \perp A C, m \angle 1=(3 x+3)^{\circ}, m \angle 2=(6 x-21) $$

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$$ x = 12 $$, $$ m \angle 1 = 39^\circ $$, $$ m \angle 2 = 51^\circ $$ Given that $$ PB \perp AC $$, we know that angles $$ \angle 1 $$ and $$ \angle 2 $$ are complementary angles, meaning their measures add up to $$ 90^\circ $$. We can set up the equation: $$ m \angle 1 + m \angle 2 = 90^\circ $$ Substituting the expressions for $$ m \angle 1 $$ and $$ m \angle 2 $$: $$ (3x + 3) + (6x - 21) = 90 $$ Now, combine like terms: $$ 3x + 6x + 3 - 21 = 90 $$ This simplifies to: $$ 9x - 18 = 90 $$ Next, add $$ 18 $$ to both sides: $$ 9x = 108 $$ Now, divide by $$ 9 $$: $$ x = 12 $$ Now that we have the value of $$ x $$, we can find the measures of $$ \angle 1 $$ and $$ \angle 2 $$. Calculating $$ m \angle 1 $$: $$ m \angle 1 = 3x + 3 = 3(12) + 3 = 36 + 3 = 39^\circ $$ Calculating $$ m \angle 2 $$: $$ m \angle 2 = 6x - 21 = 6(12) - 21 = 72 - 21 = 51^\circ $$ Thus, the measures of the angles are: $$ m \angle 1 = 39^\circ, \quad m \angle 2 = 51^\circ $$

Given \( P B \perp A C, m \angle 1=(3 x+3)^{\circ}, m \angle 2=(6 x-21) \)

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Given \( P B \perp A C, m \angle 1=(3 x+3)^{\circ}, m \angle 2=(6 x-21) \)

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