Question

XY and BD are parallel lines

X is a point on AB and C is a point on BD.
XB=XC

b) work out angle BXC Give a reason for each angle you work out

Answer 1

Explanation:

Given that,

XY//BD and XB=XC

Since, XB = XC, then ∆XBC is an isosceles triangle with angle <B = <C.

A. If an angle occupy the same relative position at each intersection where a straight line crosses two others straight lines. If the two straight lines are parallel, then the corresponding angles are equal.

To check for corresponding angle: look at if the shape form "F" shape and be sure that the lines that form the "F" shape are parallel.

So, to complete the statement,

Angle XBC = 55° because it a corresponding angle to AXY

They form a "F" and XY//BD

B. To find BXC

We know that triangle BXC is an isosceles triangle

The sum of angle in a triangle is 180°

Then,

XBC + BCX + BXC = 180°

Since, ∆XBC is isosceles then, angle <XBC = < BCX = 55°

Then,

XBC + BCX + BXC = 180°

55 + 55 + BXC = 180°

110 + BXC = 180°

BXC = 180° - 110

BXC = 70°