Given: mangletrv = 60°
mangletrs = (4x)°

prove: x = 30

3 lines are shown. a line with points t, r, w intersects with a line with points v, r, s at point r. a line extends from point r to point z between angle v r w. angle v r t is 60 degrees and angle t, r, s is (4 x) degrees.

what is the missing reason in step 3?

a 2-column table with 6 rows is shown. column 1 is labeled statements with entries measure of angle t r v = 60 degrees and measure of angle t r x = (4 x) degrees, angle t r s and angle t r v are a linear pair, measure of angle t r s + measure of angle t r v = 180, 60 + 4 x + 180, 4 x =120, x = 30. column 2 is labeled reasons with entries given, definition of a linear pair, question mark, substitution property of equality, subtraction property of equality, division property of equality.

substitution property of equality
angle addition postulate
subtraction property of equality
addition property of equality

Simonne used the following steps to simplify the given expression. 12 - 3(-2x + 4) step 1: 12 + (–3)·(–2x) + (–3)·(4) step 2: 12 + 6x + (–12) step 3: 12 + (–12) + 6x step 4: 0 + 6x step 5: 6x what property of real numbers was used to transition from step 3 to step 4? a. identity property of addition b. inverse property of addition c. associative property of addition d. commutative property of addition

Formulate alisha has a number in mind. if she adds three to her number the result is less than five. use this information to write and solve an inequality about alisha's number. then graph the solution set.

In δabc shown below, ∠bac is congruent to ∠bca: triangle abc, where angles a and c are congruent given: base ∠bac and ∠acb are congruent. prove: δabc is an isosceles triangle. when completed (fill in the blanks), the following paragraph proves that line segment ab is congruent to line segment bc making δabc an isosceles triangle. (4 points) construct a perpendicular bisector from point b to line segment ac . label the point of intersection between this perpendicular bisector and line segment ac as point d: m∠bda and m∠bdc is 90° by the definition of a perpendicular bisector. ∠bda is congruent to ∠bdc by the definition of congruent angles. line segment ad is congruent to line segment dc by by the definition of a perpendicular bisector. δbad is congruent to δbcd by the line segment ab is congruent to line segment bc because consequently, δabc is isosceles by definition of an isosceles triangle. 1. corresponding parts of congruent triangles are congruent (cpctc) 2. the definition of a perpendicular bisector 1. the definition of a perpendicular bisector 2. the definition of congruent angles 1. the definition of congruent angles 2. the definition of a perpendicular bisector 1. angle-side-angle (asa) postulate 2. corresponding parts of congruent triangles are congruent (cpctc)