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01 Jul 2022, 01:30
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If ABCD is a parallelogram, and line PQ cut its sides as shown. Which of the following must be equal to w?
(A) y + z
(B) x + z
(C) x + y
(D) 180 – z
(E) 180 – y
Are You Up For the Challenge: 700 Level Questions
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01 Jul 2022, 06:33
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As \(ABCD \) is a parallelogram, we know that \(\angle D = y^{\circ}\).
Let the vertex by \(x^{\circ} = R\). \(PRD\) is a triangle and thus \(x^{\circ} + y^{\circ} + z^{\circ} = 180^{\circ}\).
Let the vertex by \(w^{\circ} = S\). Triangle \(PSC\) is similar to triangle \(PRD\) given that lines \(BC\) and \(AD\) are parallel, and therefore have the same corresponding angles. This means that \(x^{\circ}+w^{\circ}= 180^{\circ}\).
Substituting \(x^{\circ}+w^{\circ}= 180^{\circ}\) into \(x^{\circ} + y^{\circ} + z^{\circ} = 180^{\circ}\):
\(x^{\circ} + y^{\circ} + z^{\circ} = x^{\circ}+w^{\circ}\)
\( y^{\circ} + z^{\circ} = w^{\circ}\)
Answer A
Let the vertex by \(x^{\circ} = R\). \(PRD\) is a triangle and thus \(x^{\circ} + y^{\circ} + z^{\circ} = 180^{\circ}\).
Let the vertex by \(w^{\circ} = S\). Triangle \(PSC\) is similar to triangle \(PRD\) given that lines \(BC\) and \(AD\) are parallel, and therefore have the same corresponding angles. This means that \(x^{\circ}+w^{\circ}= 180^{\circ}\).
Substituting \(x^{\circ}+w^{\circ}= 180^{\circ}\) into \(x^{\circ} + y^{\circ} + z^{\circ} = 180^{\circ}\):
\(x^{\circ} + y^{\circ} + z^{\circ} = x^{\circ}+w^{\circ}\)
\( y^{\circ} + z^{\circ} = w^{\circ}\)
Answer A
13 Jul 2022, 10:11
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Substituting [m]x^{\circ}+w^{\circ}= 180^{\circ}
How did you get this? could you please help me a bit here
How did you get this? could you please help me a bit here
