Supplementary Angles 685D07

1. **State the problem:** We are given two supplementary angles ∠1 and ∠2 with measures m∠1 = $3x + 27$ degrees and m∠2 = $8x + 21$ degrees. We need to find the measure of ∠1. 2. **Recall the rule for supplementary angles:** Supplementary angles add up to $180^\circ$. So, $$m\angle 1 + m\angle 2 = 180$$ 3. **Set up the equation:** Substitute the given expressions: $$ (3x + 27) + (8x + 21) = 180 $$ 4. **Combine like terms:** $$ 3x + 8x + 27 + 21 = 180 $$ $$ 11x + 48 = 180 $$ 5. **Isolate $x$:** $$ 11x = 180 - 48 $$ $$ 11x = 132 $$ 6. **Divide both sides by 11:** $$ x = \frac{132}{11} $$ $$ x = \cancel{\frac{132}{11}} 12 $$ 7. **Find m∠1:** Substitute $x=12$ into $3x + 27$: $$ m\angle 1 = 3(12) + 27 = 36 + 27 = 63 $$ **Final answer:** The measure of ∠1 is $63^\circ$.