The angle measurements in the diagram are represented by the following expressions

x = 8 , ∠ B = 70°

Step-by-step explanation:

∠ A and ∠ B are alternate exterior angles and are congruent, that s

8x + 6 = 4x + 38 ( subtract 4x from both sides )

4x + 6 = 38 ( subtract 6 from both sides )

4x = 32 ( divide both sides by 4 )

x = 8

Then

∠ B = 4x + 38 = 4(8) + 38 = 32 + 38 = 70°

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.