In parallelogram ABCD, AB = (2x + 15) and 4C = x. Find x.
O55
O60
O15
O45

x = 55

Step-by-step explanation:

ABCD is a paralellogram, m∠ABC = 2x + 15, m∠BCD = x

m∠ABC + m∠BCD = 180° (same side interior angles)

2x + 15 + x = 180

3x + 15 = 180 -15

3x = 165

x = 55

1,918

step-by-step explanation:

answer:   the paragraph proof is mentioned below.

step-by-step explanation:

given: in a δxwy where

such that, ∠wzx ≅ ∠yzx and zw≅zy

we have to prove that: segment zx is a perpendicular bisector of segment wy.

prove: since, zw≅zy ⇒ ∠wzy is a supplementary angle.

then, ∠wzy= 180°

⇒∠wzx + ∠yzx = 180° ( because xz divides ∠wzy into two parts)

but, ∠wzx ≅ ∠yzx ( given)

⇒∠wzy+∠wzy=180° ( by substitution)

⇒2∠wzy=180°

⇒∠wzy=90°

⇒∠wzy=∠yzx =90°

therefore, xz⊥wy where wz=zy

⇒zx is a perpendicular bisector of wy.