Question

Please help me with these two problems. It's fine if you only do one though. All help is welcomed. THANK YOU!!!

Answer 1

a) x=38

b) x=19

Explanation:

a) The interior angles at L and M can be found by subtracting 134 and 84 from 180 respectively:

∠L = 180 - 134 = 46

∠M = 180 - 84 = 96

The angles of a triangle sum up to 180, so x + 46 + 96 = 180.

From this you find that x = 180 - 46 - 96 = 38

b) Because YZ and XW are parallel, ∠Y=∠W = 2x

The sum of the angles in the triangle must be 180, so

3x-5 + 90 + 2x = 180

Which simplifies to

5x +85 = 180

5x = 95

x = 19

Answer 2

a) x = 38°; b) x = 19°

Explanation:

a)

∠OLM = 180 - 134 = 46° Supplementary angles

∠OML =180 - 84 = 96° Supplementary angles

x + 46 + 96 = 180 Interior angles of triangle

x + 142 = 180

x = 38°

===============

b)

∠XWY + 3x - 5 + 90 = 180 Interior angles of triangle

∠XWY + 3x + 85 = 180

(1) ∠XWY + 3x = 95

∠XWY = 2x

(2) ∠XWY - 2x = 0 Alternate interior angles

5x = 95 [2 subtracted from (1)]

x = 19°