By definition, two angles are supplementary if the sum of them is 180 degrees. In this case (see figure attached with the answer) the line AD is transversal to lines AB and DC. This is a proof of the Same-side interior angle theorem.
This theorem states that if we have two lines that are parallel and we intercept those two lines with a line that is transversal to both, same-side interior angles are formed, and also sum 180º, in other words, they are supplementary angles.
Then:
By the definition of a parallelogram, AB∥DC. AD is a transversal between these sides, so ∠A and ∠D are <em><u>same-side interior angles</u></em>. Because AB and DC are <em><u>parallel</u></em>, the same-side interior angles must be <em><u>supplementary</u></em> by the same-side interior angles theorem. Therefore, ∠A and ∠D are supplementary.
Andrew answered 34 questions correctly.
I got the answer by divided the 85% by 100% (100% because it's the total percentage.) I received 0.85 when dividing that. Then, I took the 0.85 and divided it by the total of 40 questions, and that gave me the answer of 34.
Answer:
In linear expresiion 3 is the coefficient
X will be the variable and -15 will be the constant term.
22 True For all real Numbers A and B, A - B = -B + A
23 True For all real Numbers P, Q, and R, P - Q - R = P - R - Q
24) True For all real Numbers X, Y, Z and (X + Y ) + Z = Z + (X + Y)
25) False For all real Numbers M and N, M/M * N = N/N ==> Example: 5/5 * 3 ≠ 3/3 * 5
26) Examples:
Counterexamples =====> 5 - 0 = 5; 5/1 = 5
5 - 3 ≠ 3 - 5; (5 - 3 ) - 2 ≠ 5 - (3 - 2 );
6/3 ≠ 3/6; (24/6 )/2 ≠ 24/ (6/ 2 )
Hope that helps!!!! : )
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