Complete the proofs below by filling in the missing statements and reasons. 10. Given: 21 and 22 form a linear pair;

21 and 23 are supplementary

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2

3

Prove: 22 23

Statements

Reasons

1. Z1 and 2 form a linear pair

1.

2. 21 and 22 are supplementary

2.

3.

mZ1 + m2 = 180°

3.

4. Z1 and 23 are supplementary

4.

5.

mZ1 + m23 = 180°

5.

6.

m21 + m2 = mZ1 + m23

6.

7. m2 = m_3

7.

8. Z2 Z3

3901918.

dc=6 square root of 3 and ac is 12 square root 3

c and d

step-by-step explanation:

square root of 3/2 = 18/c

cross multiply to get 18*2=√3*c

36/√3 * √3/√3 = c

c= 36*√3/3

c=12√3

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step-by-step explanation:

1. 180°. the sum of the interior angles of a triangle is 180°, for the equilateral triangle that it has three equals side is 60°+60°+60°=180°.

2. 60°. each interior angle of a equilateral triangle is 60°

3. 120°. the measure of ∠m is 120°, the sum of the angles ∠m and ∠n is equal to 180°. so, in order to find the measure of ∠m, we have ∠m+∠n=180° > ∠m=180°-∠n > ∠m=180°-60°=120°.

4. 360°. the sum of the exterior angles of an equilateral triangle is ∠m+∠r+∠x=120°+120°+120°=360°. the exterior angles of any triangle always add 360°.