Question

XY and BD are parallel lines.
X is a point on AB and C is a point on BD.
XB = XC.
a) complete this sentence.
Angle XBC = 55 Degrees Because . . .
b) Work out angle BXC.
give a reason for each angle you work out.
. . .
Pls Help me

Answer 1

Given : XY ║AB

Solution :

(a) if XY ║AB ad AB is the transversal line

then

∠AXY = ∠XBC (Corresponding angles )

now ,

(b) since XB = XC

XBC is the isosceles triangle

therefore

∠XBC = ∠XCB (angle opposite to equal side are equal )

now , in triangle XBC

∠XBC  + ∠XCB + ∠BXC = 180° (angle sum property)

55 + 55 + ∠BXC = 180°

∠BXC = 180°- 110°

∠BXC = 70°

hence , ∠BXC = 70°

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