Question

Find x if m/ABC = 160°,
m/UBC = 12x + 2,
and mLABU = 11x - 3.

Answer 1

x=4

Explanation:

We can use the law of sines to find x.First, let's find m/UBC. Using the law of sines on triangle ABU, we have:

sin(m/ABU) / BU = sin(m/UBC) / AU

Since mLABU = 11x - 3, m/ABU = (180 - 11x + 3)/2 = 86 - 5.5x

So, sin(86 - 5.5x) / BU = sin(12x + 2) / AU

Next, using the law of sines on triangle ABC, we have:sin(m/ABC) / BC = sin(m/ABU) / AU

Since m/ABC = 160°, sin(160) / BC = sin(86 - 5.5x) / AU

We can equate the two expressions for sin(m/ABU) / AU and simplify to solve for x:

sin(160) / BC = sin(12x + 2) / AU

sin(86 - 5.5x) / BU = sin(12x + 2) / AU

BC * sin(12x + 2) = BU * sin(160)

Solving for x, we find that x = 4.

Correct me if I’m wrong.