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
Mark this and return

Answer 1

The missing reason in step 3: is vertical angles are congruent, while the missing reason in step 5 is: definition of congruency.

What are Vertical Angles?

Two angles are referred to as vertical angles is:

• They share the same vertex angle.
• They are non-adjacent angles.
• They do not share a common side.

What is the Vertical Angles Theorem?

According to the vertical angles theorem, two angles that are vertical angles must be congruent to each other, that is, they are equal in measure.

In the image given, as attached below, angle EDF and angle ADC are vertical angles pair. Therefore, based on the vertical angles theorem, they have equal measure (they are congruent to each other).

Thus, the missing reason in step 3: is vertical angles are congruent, while the missing reason in step 5 is: definition of congruency.

Learn more about vertical angles on:

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