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/_1 and /_2 are omplementary angles. If m /_1=(7x+16)^(@) and m/_2=(4x-3)^(@), then find the measure of /_2. rarr(7x+16)+(4x-3) Copyright DeltaMath -3

66. ∠1 \angle 1 and ∠2 \angle 2 are omplementary angles. If m ∠1=(7x+16)∘ \angle 1=(7 x+16)^{\circ} and m∠2=(4x−3)∘ \mathrm{m} \angle 2=(4 x-3)^{\circ} , then find the measure of ∠2 \angle 2 .\newline→(7x+16)+(4x−3) \rightarrow(7 x+16)+(4 x-3) \newlineCopyright DeltaMath\newline−3 -3

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Q. 66. ∠1 \angle 1 and ∠2 \angle 2 are omplementary angles. If m ∠1=(7x+16)∘ \angle 1=(7 x+16)^{\circ} and m∠2=(4x−3)∘ \mathrm{m} \angle 2=(4 x-3)^{\circ} , then find the measure of ∠2 \angle 2 .\newline→(7x+16)+(4x−3) \rightarrow(7 x+16)+(4 x-3) \newlineCopyright DeltaMath\newline−3 -3
  1. Set up equation: Complementary angles add up to 9090 degrees, so set up the equation (7x+16)+(4x−3)=90(7x+16) + (4x-3) = 90.
  2. Combine like terms: Combine like terms: 7x+4x+16−3=907x + 4x + 16 - 3 = 90.
  3. Simplify equation: Simplify the equation: 11x+13=9011x + 13 = 90.
  4. Subtract 1313: Subtract 1313 from both sides: 11x=90−1311x = 90 - 13.
  5. Calculate new value: Calculate the new value: 11x=7711x = 77.
  6. Divide by 1111: Divide both sides by 1111: x=7711x = \frac{77}{11}.
  7. Solve for x: Solve for x: x=7x = 7.
  8. Substitute xx back: Now, substitute xx back into the expression for m/2m /_2: m/2=(4x−3)∘m /_2 = (4x - 3)^\circ.
  9. Plug in value: Plug in the value of xx: m/2=(4(7)−3)∘m /_2 = (4(7) - 3)^\circ.
  10. Calculate measure: Calculate the measure: m/2=(28−3)∘m /_2 = (28 - 3)^\circ.
  11. Final calculation: Final calculation: m/2=25∘m /_2 = 25^\circ.

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