Question

Please answer for 13

Answer 1

a) 2x+36=5x from the exterior angle property.
3x=36
x=12.
b)from the property that equal sides have equal angles
  40 + 180-y + 180-y = 180
220-2y=0
220=2y
y=110.

c)135+y = 180  linear angle property.
y=180-135
y=45

exterior angle property
85+45=x
130 =x.

Answer 2

i ) |_36 + |_2x = 5x ( exterior angle property )

36 = 5x - 2x

36 = 3x

12 = x


ii ) Angle opposite to equal side are equal .

AB = BC

|_ABC = |_ACB

Let angle |_ ACB be y

In ∆ ABC

using angle sum property of ∆

|_ABC + |_ACB + |_ BAC = 180

y + y + 40 = 180

2y = 180 - 40

2y = 140

y = 70

|_ABC + |_BAC = |_ACD ( exterior angle property )

70 + 40 = x

110 = x


iii ) |_y + |_135 = 180 ( linear pair )

y = 180 - 135

y = 45

|_ B + |_y = |_ x ( exterior angle property )

85 + 45 = x

130 = x