geometry constructions

How do you construct a scalene triangle ABC where m<A=45 degrees and m<B=30 degrees?

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  1. A scalene triangle is a triangle that has three unequal sides.

    The question is asking you to draw a scalene triangle. Label its vertices (where its sides meet) A, B, and C. Then, mark angle A 45 degrees and angle B 30 degrees. You can also label angle C using the property that all triangles have angles that add up to 180 degrees.

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  2. Construction:
    Make a perpendicular bisector (90 deg). Bisect that angle to get 45.

    Now you have one angle. For the 30 deg angle, set your compass to some arbitrary length. measure up the perpendiculare bisector that arbitrary length, mark that arc, and measure from that arc up the length again. Set you compass now for that double distance, and measuring from the first arc (the first arc mark), cast an arc across the base line . You have constructed a 30 degree angle (side opposite 1/2 of the hypotenuse).
    connect the 45 degree line to the line coming from the vertex of the 30 degree angle, and you have it.

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