Question

Given: mAngleADE = 60° and mAngleCDF = (3x + 15)°

Prove: x = 15

3 lines are shown. A line with points E, D, C intersects a line with points A, D, F at point D. A line extends from point D to point B between angle A D C. Angle F D C is (3 x + 15) degrees and angle E D A is 60 degrees.
What is the missing statement and the missing reason in step 5?

A 2-column table with 7 rows. Column 1 is labeled statements with the entries measure of angle A D E = 60 degrees and measure of angle C D F = (3 x + 15) degrees, angle A D E and angle C D F are vertical angles, angle A D E is-congruent-to angle C D F, measure of angle A D E = measure of angle C D F, question mark, 45 = 3 x, and, 15 = x. Column 2 is labeled reasons with the entries given, definition of vertical angles, vertical angles congruent, definition of congruency, question mark, subtractive property, division property.

Statement: 60 = 3x + 15; Reason: substitution
Statement: x = 15; Reason: subtraction property of equality
Statement: 60 = 3x + 15; Reason: transitive property
Statement: x = 15; Reason: subtraction and division properties of equality


Answer is NOT option B.

Answer 1

The missing statement in step 5 of the proof is "60 = 3x + 15" and the missing reason is the "Transitive Property of Equality," which justifies that the measures of vertical angles are equal and thus can be set equal to each other to solve for x.

Step-by-step explanation:

The question requires determining the missing statement and reason in a geometry proof where vertical angles are concerned. Given that mAngleADE = 60° and mAngleCDF = (3x + 15)°, and that these angles are vertical angles, they must be congruent. The next step (step 5) in proving that x = 15 should logically be equating these two angle measures and solving for x.

The correct missing statement for step 5 is: 60 = 3x + 15; and the missing reason is: Transitive Property of Equality (since mAngleADE = mAngleCDF, and mAngleADE = 60°, then by transitive property, 60° = 3x + 15°).

After that, using the Subtraction and Division Properties of Equality, one would solve for x, obtaining x = 15.

Answer 2

Your answer shall be A. Statement: 60 = 3x + 15; Reason: substitution

Step-by-step explanation:

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