Question

Please help with this. I only need help with the first question I have the second one figured out,

Answer 1

Answer:

m∠WZX = 41°

Step-by-step explanation:

diagonals bisect angles and opposite angles are congruent

therefore, ∠WXY ≅ ∠WZY

∠WZY must equal [360 - 2(68)] ÷ 2 which equals 112°

If ∠WXZ = 71° then so does ∠XZY

Which means that ∠WZX must equal 112-71 which is 41°

Answer 2

Answer:  41 degrees

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Explanation:

Refer to the diagram below. I've marked up the figure with various angles to point out the angles we'll be working with.

• angle XYZ = 68 in green
• angle WXZ = 71 in red
• angle WZX = unknown, in blue

To make things a bit simpler in terms of notation, and to match up colors with variable letters, I'm going to use the following

• R = red angle
• G = green angle
• B = blue angle

Notice how the two red angles I've marked up are alternate interior angles. This works because WX is parallel to ZY. Also notice that the red and blue angles combine to form the angle WZY, which is adjacent to angle XYZ in green.

For any parallelogram, the adjacent angles always add to 180.

(angle WZY) + (angle XYZ) = 180

(blueAngle+redAngle) + (greenAngle) = 180

(B+R) + (G) = 180

(B+71) + (68) = 180

B+139 = 180

B = 180-139

B = 41

The blue angle is 41 degrees, which means angle WZX is 41 degrees

Side note: Your steps and answer to problem 11 are correct. Nice work.