Answer:
a) angle XBC=55° because corresponding angles are congruent.
b) <BXC=70°
Step-by-step explanation:
From the diagram, XY and BD are parallel lines.
This means line AB is a transversal .
Angle XBC and angle AXY form an F-angle.
F-angles are also called corresponding angles, and are congruent.
Therefore, angle XBC=55° because corresponding angles are congruent.
b) We want to work out, angle BXC.
Since XB=XC, triangle XBC is isosceles.
The base angles of an isosceles triangles are equal.
This implies that:
<XBC=<BCX=55°.
Also, sum of angles in a triangle add up to 180°.
<XBC+<BCX+<BXC=180°
55°+55°+<BXC=180°
<BXC=180°-55°-55°
<BXC=180°-110°
<BXC=70°
