Answer :

Answer:

80 degrees

Step-by-step explanation:

4x+3x+2x=180(ASP of Triangle)

9x=180 => x=20degree

4x=angle BCD (Alternate Interior angles)

80degree = angle BCD

Answer:

m∠BCD = 80°

Step-by-step explanation:

The interior angles of a triangle sum to 180°. Therefore, in triangle ABC:

[tex]m\angle CAB + m\angle ABC + m\angle BCA = 180^{\circ} \\\\3x + 4x + 2x = 180^{\circ}[/tex]

Solve for x:

[tex]9x = 180^{\circ} \\\\\dfrac{9x}{9}=\dfrac{180^{\circ}}{9}\\\\x=20^{\circ}[/tex]

So, the measures of each angle of triangle ABC are as follows:

[tex]m\angle CAB = 3x = 3 \cdot 20^{\circ}=60^{\circ} \\\\ m\angle ABC = 4x = 4 \cdot 20^{\circ}=80^{\circ} \\\\ m\angle BCA = 2x = 2 \cdot 20^{\circ}=40^{\circ}[/tex]

Given that line segments AB and CD are parallel in the provided figure, and BC acts as a transversal intersecting these parallel lines, angles BCD and ABC are alternate interior angles.

According to the Alternate Interior Angles Theorem, when two parallel lines are intersected by a transversal, the alternate interior angles formed are congruent. Therefore, in this case, m∠BCD = m∠ABC.

Since we have already calculated that m∠ABC = 80°, then:

[tex]\LARGE\boxed{\sf m\angle BCD = 80^{\circ}}[/tex]