Question

Xy and bd are parralel lines x is point on ab and c is a point on bd xb=xc work out angle bxc give a reason for each angle you work out

Answer 1

Given:

Xy and bd are parralel lines x is point on ab and c is a point on bd.

xb=xc.

To Find:

Angle bxc.

Solution:

We can see that XY is parallel to BD.

AB is a line intercepting both these lines.

Therefore,

• ∠AXY = ∠XBC , as they are corresponding angles.
• ∠XBC = 55°.

Now for other angles,

ΔXBC is isosceles triangle.

• ∠XBC = ∠XCB
• ∠XCB= 55°
• ∠CXB = 180° - 2 x 55° = 70°

Also ∠AXY +∠YXC + ∠CXB = 180°

Therefore

• ∠YXC = 180° - 70° - 55° = 55°

Now,

• ∠XCD = ∠CBX + ∠CXB ,
• Exterior angle of a triangle is the sum of internal opposite angles.
• ∠XCD = 125°

Therefore, ∠BXC = 55°