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
Statement: x =15.
Reason: Subtraction and Division properties of equality.
⇒ 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;
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
x=15 Hence proved!
The answer is: A) Statement: 60 = 3x + 15; Reason: substitution
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at least two
m∠5 + m∠3 = m∠1 is true.
m∠5 + m∠6 = 180 is true
m∠2 +m∠3 = m∠6 is true
m∠2 +m∠3 +m∠5 = 180 is true