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2 answers:
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.
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Step-by-step explanation:
This question utilizes combining like terms and common denominators. First you have to convert both terms including "a" to have a denominator of 8. You would do this by multiplying both the numerator, and the denominator by the same value. This value in the case of would be 2, and in the case of
the value would be 2. This would result in the equation:
. Then simply combine like terms to get your final answer.