# 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

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### 2 Answers

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:

**Sources:**

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.