Question

Given a convex quadrilateral ABCD with m∠A = (x + 10)º, m∠B = (y + 40)º, and m∠C = (3x − 20)º.

ABCD is a parallelogram if x = 15 and y = 115

Answer 1

The given quadrilateral ABCD is not a parallelogram when x = 15 and y = 115.

Step-by-step explanation:

A quadrilateral ABCD is a parallelogram if and only if opposite sides are parallel and congruent.

Let's look at the given angles: m∠A = (x + 10)º, m∠B = (y + 40)º, and m∠C = (3x - 20)º.

If x = 15 and y = 115, we can substitute these values into the angle measures:

m∠A = (15 + 10)º

= 25º

m∠B = (115 + 40)º

= 155º

m∠C = (3(15) - 20)º

= 25º

Since m∠A = m∠C, we can conclude that angle A is congruent to angle C.

However, angle B is not congruent to either angle A or angle C.

Therefore, the given quadrilateral ABCD is not a parallelogram when x = 15 and y = 115.