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Answer:
a) Angle XBC = 55° because corresponding angles are equal.
b) Angle BXC = 70°
Step-by-step explanation:
The image of the complete question is attached to this solution.
a) Angle XBC = 55° because....
Line XY and BD are parallel.
A straight line, AB, crosses the two parallel lines, thereby making angles AXY and XBC corresponding angles because they occupy the same relative position at points where the straight line, AB, intersects the two lines XY and BD.
Since the two lines, XY and BD, are parallel, the corresponding angles related to them are said to be equal.
b) Angle BXC
Since we have found and confirmed that angle XBC is truly 55°.
Triangle BXC is an isosceles triangle, with sides BX and XC equal, the base angles XBC and BCX are both equal.
Angle XBC = Angle BCX = 55° (base angles of an isosceles triangle are equal)
Then, the sum of angles in a triangle = 180°
Hence,
(Angle XBC) + (Angle BCX) + (Angle BXC) = 180° (sum of angles in a triangle)
55° + 55° + Angle BXC = 180°
Angle BXC = 180° - 110° = 70°
Hope this Helps!!!
