Question

∠1 and ∠2 are complementary angles. if m∠1 = (5x + 7)° and m∠2 = (4x + 10)°, then x = ?

Explanation:

Step1: Recall complementary angles sum to 90°

Since ∠1 and ∠2 are complementary, \( m\angle1 + m\angle2 = 90^\circ \). Substitute the given expressions: \( (5x + 7) + (4x + 10) = 90 \).

Step2: Combine like terms

Combine the x terms and constant terms: \( 5x + 4x + 7 + 10 = 90 \), which simplifies to \( 9x + 17 = 90 \).

Step3: Solve for x

Subtract 17 from both sides: \( 9x = 90 - 17 = 73 \)? Wait, no, 90 - 17 is 73? Wait, 90 - 17 is 73? Wait, 90 - 17: 90 - 10 is 80, 80 -7 is 73? Wait, no, wait 5x +4x is 9x, 7 +10 is 17. So 9x +17 =90. Subtract 17: 9x = 90 -17 =73? Wait, that can't be. Wait, no, 90 -17 is 73? Wait, 17 +73 is 90. Then x = 73/9? That can't be right. Wait, did I make a mistake? Wait, 7 +10 is 17? Wait, 7 +10 is 17. 90 -17 is 73. Then 9x=73, x=73/9≈8.11? But that seems odd. Wait, maybe I misread the problem. Let me check again. The problem says ∠1 and ∠2 are complementary. m∠1=(5x+7)°, m∠2=(4x+10)°. So sum is 90. So 5x +7 +4x +10 =9x +17=90. Then 9x=90-17=73. So x=73/9≈8.11. But that's a fraction. Wait, maybe the problem was supplementary? No, the problem says complementary. Wait, maybe I made a mistake in addition. 7 +10 is 17. 90 -17 is 73. 73 divided by 9 is 73/9. Wait, but maybe the problem has a typo? Or maybe I misread the angles. Wait, let me check again. 5x +7 and 4x +10. Sum to 90. So 9x +17=90. 9x=73. So x=73/9. So that's the answer.

Wait, but maybe I made a mistake. Let me recalculate. 5x +7 +4x +10 = (5x +4x) + (7 +10) =9x +17. Set equal to 90. 9x =90 -17=73. So x=73/9≈8.11. So that's the solution.

Answer:

\( \boxed{\dfrac{73}{9}} \) (or approximately 8.11, but exact form is 73/9)