I NEED THIS DONE, PLEASE SHOW ALL WORK!! PICTURE 1 IS FOR QUESTION 3 AND PICTURE 2 IS FOR QUESTION 2. THANK YOUfill in the blanks in the following proof:1. given: 4x=8(x-2)prove: x = 4statement — reason1. 4x=8(x-2) — 1.2. — 2. distributive property3. -4x = -16 — 3.4. x = 4 — 4.2. write a paragraph for the following conjecturegiven: m < SQR = 55°m < PQS = 35°prove: △PQR is a right triangle3. write a paragraph proof, flowchart, or 2 column proof for the followinggiven: m < 1 = 27°, < 1 ^ < 2 are supplementaryprove: m < 2 = 153°

Accepted Solution

Answer:See explanationStep-by-step explanation:Question 1. Write two-column proof.        Statement                   Reason1. [tex]4x=8(x-2)[/tex]                    Given2. [tex]4x=8x-16[/tex]                   Distributive Property of Equality3. [tex]4x-8x=8x-8x-16\\ \\-4x=-16[/tex] Subtraction Property of Equality4. [tex]x=4[/tex]                            Division Property of EqualityQuestion 2.                    Statement                                 Reason1. [tex]m\angle SQR = 55^{\circ}[/tex]                           Given2. [tex]m\angle PQS = 35^{\circ}[/tex]                          Given3. [tex]m\angle SQR+m\angle PQS=m\angle PQR[/tex]  Angle Addition Postulate4. [tex]m\angle PQR=55^{\circ}+35^{\circ}\\ \\m\angle PQR=90^{\circ}[/tex]  Substitution Property of Equality5. [tex]\angle PQR[/tex] is a right angle    Definition of a right angle6. [tex]\triangle PQR[/tex] is a right triangle   Definition of a right triangleQuestion 3:                   Statement                                 Reason1. [tex]\angle 1[/tex] and [tex]\angle 2[/tex] are supplementary                                 Given2. [tex]m\angle 1+m\angle 2=180^{\circ}[/tex]  Definition of supplementary angles3. [tex]m\angle 1=27^{\circ}[/tex]       Given4. [tex]27^{\circ}+m\angle 2=180^{\circ}[/tex]   Substitution Property of Equality5. [tex]27^{\circ}-27^{\circ}+m\angle 2=180^{\circ}-27^{\circ}\\ \\m\angle 2=153^{\circ}[/tex]   Subtraction Property of Equality