Ana baked 82 muffins for her school’s bake sale. She put 4 muffins aside for
2 answers:
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First option: correct. This is because angles WOX and XOZ are supplementary, so
Second option: correct. By the inscribed angles theorem, we have
Angles WOX and YOZ are congruent because they form a vertical pair; they both have measure 76 degrees. This means angles WXY and WZY are also congruent, since the interior angles of any triangle sum to 180 degrees in measure. Therefore triangles WXO and YZO form a side-side-side pair, and all SSS triangles are similar.
Third option: not correct. There is a theorem (not sure what the name is) regarding intersecting chords that asserts the average of the measures of arcs WY and XZ is the same as the measure of angle XOZ. This means
Fourth option: not correct. This is because arcs WX and XZ are not "supplementary" in the sense that they do not form a semicircle and their measures do not add to 180 degrees. We know this because it's clear that point O is not the center of the circle. If it was, then angle XOZ would be a central angle and its measure would be the same as the arc XZ it subtends.
Fifth option: correct. The theorem mentioned in the assessment of the third option makes itself useful here. We have
To answer this, you will represent the new side length of the square as x + 6.
To find the area you will multiply (x + 6) by (x + 6).
To do this, you will multiply x and x, x by 6 twice and 6 by 6.
See the attached picture for the expression representing the area of the new square.
To find the area you will multiply (x + 6) by (x + 6).
To do this, you will multiply x and x, x by 6 twice and 6 by 6.
See the attached picture for the expression representing the area of the new square.