Question

Given \qquad \overline{OL}\perp\overline{ON} OL ⊥ ON start overline, O, L, end overline, \perp, start overline, O, N, end overline \qquad m \angle LOM = 3x + 38^\circm∠LOM=3x+38 ∘ m, angle, L, O, M, equals, 3, x, plus, 38, degrees \qquad m \angle MON = 9x + 28^\circm∠MON=9x+28 ∘ m, angle, M, O, N, equals, 9, x, plus, 28, degrees Find m\angle LOMm∠LOMm, angle, L, O, M:

Answer 1

Given:

• OL ⏊ ON
• m∠ LOM = 3x + 38°
• m∠ MON = 9x + 28°

To find: m∠ LOM = ?

Solution:

Given, OL is perpendicular to ON.

∴ m∠ LON = 90°

⇒ m∠ LOM + m∠ MON = 90°

⇒ (3x + 38°) + (9x + 28°) = 90°

⇒ 3x + 38° + 9x + 28° = 90°

⇒ 12x + 66° = 90°

⇒ 12x = 90° - 66°

⇒ 12x = 24°

⇒ x = 2°

∴ m∠ LOM = 3 (2°) + 38°

= 6° + 38°

= 44°

Answer 2

Answer:

57

Step-by-step explanation:

Correct on Khan academy.