Question

X is in the interior of ∠LIN. m∠LIN=100, m∠LIX=14t, and m∠XIN=x+10. What is the value of t? What are m∠LIX and m∠XIN?

a. t=10, m∠LIX=140, m∠XIN=x+10

b. t=7, m∠LIX=98, m∠XIN=x+10

c. t=5, m∠LIX=70, m∠XIN=x+10

d. t=14, m∠LIX=196, m∠XIN=x+10

Answer 1

X is in the interior of ∠LIN. m∠LIN=100, m∠LIX=14t, and m∠XIN=x+10. m∠LIX and m∠XIN is b. t=7, m∠LIX=98, m∠XIN=x+10

Step-by-step explanation:

To determine the value of t, we utilize the information that m∠LIN = 100, m∠LIX = 14t, and m∠XIN = x + 10 within the interior of ∠LIN. The sum of the angles in a linear pair is 180°, so m∠LIN + m∠LIX = 180°. Substituting the given values, we get m∠LIN + 14t = 180, which simplifies to 14t = 80, leading to t = 5.

With t = 5, we can find m∠LIX by substituting t into the expression 14t, resulting in m∠LIX = 14 × 5 = 70°. Similarly, m∠XIN is determined by x + 10, and as m∠LIN = 100°, m∠XIN + m∠LIX = 180°. Substituting the known values, we have x + 10 + 70 = 180, leading to x = 100.

Therefore, the correct answer is option b. t = 7, m∠LIX = 98°, and m∠XIN = x + 10 = 110°. This aligns with the conditions given and satisfies the angle relationships within ∠LIN, providing a consistent and accurate solution.