Question

In △LUV, UV¯¯¯¯¯¯¯¯=UL¯¯¯¯¯¯¯ and the measure of ∠U=42.6°. The measure of ∠L=(3x+y)°and the measure of ∠V=(4x−3y−0.8)°. Find the value of x.

21.2

18.8


40.4


32.1

Answer 1

x = 34.06

Explanation:

The sum of angles in the triangle LUV is 180 degrees

Given

∠L=(3x+y)°

∠U=42.6°

∠V=(4x−3y−0.8)°

Since ∠L+∠U + ∠V = 180 degrees

Substitute:

3x+y + 42.6 + 4x - 3y - 0.8 = 180

7x - 2y - 41.8 = 180

7x - 2y = 221.8 ... 1

Since UV = UL, hence the triangle is isosceles and <V = <L

3x+y = 4x-3y - 0.8

-x +4y = -0.8

x - 4y = 0.8 ....2

From 2: x = 0.8+4y

Substitute into 1:

7x - 2y = 221.8

7(0.8+4y) - 2y = 221.8

5.6 + 28y-2y = 221.8

26y = 221.8-5.6

26y = 216.2

y = 8.32

Get x

x = 0.8+4y

x = 0.8+4(8.32)

x = 0.8 + 33.26

x = 34.06

Note that it was assumed that <V = <l since the question is not clear