# Video: US-SAT03S3-Q11-520163054125

In the figure, lines π, π, and π intersect at a point. If π₯ + π§ = π€ + π’, which of the following must be true? i. π§ = π’, ii. π₯ = π¦, iii. π¦ = π‘. [A] ii and iii only [B] i and ii only [C] i and iii only [D] i, ii, and iii

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### Video Transcript

In the figure, lines π, π, and π intersect at a point. If π₯ plus π§ equals π€ plus π’, which of the following must be true? 1) π§ equals π’, 2) π₯ equals π¦, or 3) π¦ equals π‘. A) 2 and 3 only, B) 1 and 2 only, C) 1 and 3 only, or D) 1, 2, and 3.

Weβre going to consider which of these angles are equal to each other. Before we do that, letβs go ahead and highlight angles that we already know are equal to one another. When two lines intersect, opposite angles are equal to one another. We know that π₯ must be equal to π‘ and that π¦ is equal to π’ and π§ is equal to π€. Our question told us that π₯ plus π§ equals π€ plus π’. π₯ plus π§ equals π€ plus π’. We know that π€ and π§ are equal. And that means we could substitute π€ for π§.

If we have a π€ on both sides of our equation, it cancels out. And that tells us that π₯ is equal to π’. And we know that π₯ is equal to π‘ and that π’ is equal to π¦. Our yellow angles are the same size as the pink angles. If we make π¦ and π’ yellow, itβs easier to identify which of our three statements must be true.

Is π§ equal to π’? We canβt say that thatβs true based on the given information. Is π₯ equal to π¦? It is. And is π¦ equal to π‘? That also must be true based on our given information. 2 and 3 are true. And so, we select option A, 2 and 3 only.