Question

page one: 4 pts each (you must get 7 correct to earn 28 points in this section)
1.) solve for m∠edm. (show your work)
a.) 84°
b.) 134°
c.) 170°
d.) 142°
2.) which value of x would make u||v?
a.) 6
b.) -6
c.) 9
d.) -9
which of these statements is true?
a.) ∠2 and ∠8 are corresponding angles.
b.) ∠4 and ∠5 are corresponding angles.
c.) ∠7 and ∠3 are corresponding angles.
d.) ∠8 and ∠6 are corresponding angles.
solve for m∠edf. (this question is not multiple choice. show your work.)

Explanation:

Step1: Find m∠EDM in the first triangle

In a triangle, the sum of interior angles is 180°. In triangle EFD, we know two angles: ∠F = 96° and ∠E=46°. First, find ∠EDF. Let ∠EDF = x, then x=180°-(96° + 46°)=180° - 142° = 38°. Since ∠EDM is a straight - line adjacent to ∠EDF, and a straight - line angle is 180°, m∠EDM=180° - 38°=142°.

Step2: Find x for u||v

If u||v, then the corresponding angles are equal. The angle 10x + 15 and 75° are corresponding angles. So, 10x+15 = 75. Subtract 15 from both sides: 10x=75 - 15=60. Divide both sides by 10: x = 6.

Step3: Identify corresponding angles

Corresponding angles are in the same relative position with respect to the transversal and the parallel lines. When two parallel lines are cut by a transversal, ∠2 and ∠6, ∠1 and ∠5, ∠3 and ∠7, ∠4 and ∠8 are corresponding angles. So, none of the options A, B, C, D are correct for corresponding - angle relationships as given. But if we assume a mis - typing and consider the general concept, we know the rules for corresponding angles.

Step4: (No information for m∠EDF in the fourth part as no relevant figure details are clear enough to solve)

Answer:

1. D. 142°
2. A. 6
3. None of the above (based on correct corresponding - angle concept)