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 1

The answer is:    A) Statement: 60 = 3x + 15; Reason: substitution

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Answer 2

Answer:

Statement: x =15.

Reason: Subtraction and Division properties of equality.

Explanation:

Given:  and  

⇒  

⇒ 60= 3x+15 or

Subtraction property of equality: Subtract the same number from both sides of an equation.

Subtract 15 from both sides of an equation;

 or

45=3x

Division property of equality: Divide the same number from both sides of an equation;

Divide by 3 from both sides of an equation, we have

Simplify:

x=15        Hence proved!