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.

Respuesta :

Answer:

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

Explanation:

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The Statement: x = 15; Reason: subtraction and division properties of equality can be marked as true. Thus, the correct option is D). Statement: x = 15; Reason: subtraction and division properties of equality.

What is subtraction and division properties of equality?

The subtraction property of equality refers to balancing an equation by applying the same mathematical operation on both the sides of an equation.

The division property of equality refers to balancing an equation when both sides of an equation is divided by the same non-zero number and the two sides remain equal.

Given Statement is x =15,

Explanation by using Subtraction and Division properties of equality:

According to the question: 60= 3x+15

Subtraction property of equality: Subtract the same number i.e. 15 from both sides of an equation: 60= 3x+15

                                            45=3x

Division property of equality: Divide the same number from both sides of an equation:  45=3x

Divide by 3 from both sides of an equation, we will get:  45 = 3x

                                                                                               15 = x

Hence, proved x = 15.

Learn more about division properties here:-

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