solve with statements and reasons using a +(plus) shape.  #3 is in the top right quadrant, #6 is in the lower left quadrant. #4 is in the lower right quadrant and #1 is in the upper left...

 solve with statements and reasons using a +(plus) shape.  #3 is in the top right quadrant, #6 is in the lower left quadrant. #4 is in the lower right quadrant and #1 is in the upper left quadrant.  A line travels through at a slant dividing the #1 quadrant and continues to the #4 quadrant at  slant dividing it in half.

I have the pair of vertical angles as <2 and <5             (< means angle)

I have a pair of complementary angles as <2, <1

I have a pair of supplementary angles as <3, <6

this is what I need help with:

Statements                                                         Reasons

1. <1 = <2                                                              Given

2. <2 = <5                                                               ??

3.  ??                                                                       Transitive Propertyof Angle congruence

4.  m<1 = m<5                                                        ??

5.  if m<1 = 60 degrees, then m<3 + m<5 = ??

thank you

Asked on by marley112

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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted on

1. `\angle 1 \cong \angle 2 `                          1. Given

2. `\angle 2 \cong \angle 5 `                        2. Vertical angles are congruent

3. `\angle 1 \cong \angle 5 `                           3. Transitive property of congruence

4. `m \angle 1 = m \angle 5 `                  4. Definition of congruent angles

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Question 5 does not conform to your description of the diagram. If angle 1 and angle 2 are complements, and angle 1 is congruent to angle 2, then each has measure 45 degrees.

Assuming that we no longer have angle 1 congruent to angle 2, but the angles are still complements and assuming angles 3 and 6 are supplementary we can answer question 5 as follows:

If the measure of angle 1 is 60, then the measure of angle 2 is 30 since they are complements. Angles 2 and 5 are congruent since they are vertical angles, so the measure of angle 5 is 30 degrees. From the diagram, angle 3 and angle 6 must have measure 90 (they form a straight line with the angle formed by angle 1 and angle 2).

So `m \angle 1 =60 ==> m \angle 3 + m angle 5 = 120^@ `

I assume the diagram is something like the attached:

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marley112 | (Level 1) Honors

Posted on

your image is close.  #1 and #2 need to flip.  #5 goes to the blank quadrant, then #4 goes to where #5 was.  I hope this helps.

embizze's profile pic

embizze | High School Teacher | (Level 1) Educator Emeritus

Posted on

The relative positions of angles 1,2 and 3,4 will not matter to the answer as long as angles 2 and 5 remain vertical angles.

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