a) Angle XBC = 55° because it forms corresponding angle with angle AXY.
b) angle BXC = 70°
What are parallel lines?
"The lines in the same plane that are at equal distance from each other and never meet."
What is transversal?
"It is a line that passes through two lines in the same plane and intersects two distinct points."
What is isosceles triangle?
- "It is a triangle that has any two sides equal in length."
- "The angles opposite to equal sides are equal in measure."
What are corresponding angles?
"The angles which that formed in matching corners with the transversal when two parallel lines and the transversal intersects."
What are alternate interior angles?
"They lie on the inner side of the parallel lines but on the opposite sides of the transversal. "
For given question,
Here, ∠AXY = 55°
line XY an BD are parallel lines and line AB is a transversal.
We can observe that, ∠AXY and ∠XBC are corresponding angles.
We know, if a transversal intersects two parallel lines, then each pair of corresponding angles is equal.
⇒ ∠AXY = ∠XBC
⇒ ∠XBC = 55°
Also, we can observe that triangle BXC is an isosceles triangle.
⇒ ∠XBC = ∠XCB
⇒ ∠XCB = 55°
From figure,
⇒ ∠XCB = ∠CXY ......................(alternate interior angles)
⇒ ∠CXY = 55°
We know, the sum of all angles on either side of the line is 180°.
⇒ ∠AXY + ∠YXC + ∠BXC = 180°
⇒ 55° + 55° + ∠BXC = 180°
⇒ ∠BXC = 70°
Therefore, a) Angle XBC = 55° because it forms corresponding angle with angle AXY.
b) angle BXC = 70°
Learn more about angles formed by parallel lines and transversal here:
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