Question

The measure of anglerst can be represented by the expression (6x 12)°. three lines extend from point s. the space between lines s r and s u is 78 degrees. the space between lines s u and s t is 3 x minus 12. what is manglerst in degrees? 78° 84° 120° 156°

Answer 1

∠RST = 120°

Explanation:

We assume the positions of the lines and angles will match the attached figure. The angle addition theorem gives a relation that can be solved for x, then for the value of angle RST.

∠RSU +∠UST = ∠RST

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78° + (3x -12)° = (6x +12)° . . . . . substitute given values into the above

54 = 3x . . . . . . . . . . . . . . . . divide by °, subtract 3x+12

108 = 6x . . . . . . . . . . . multiply by 2

120° = (6x +12)° = ∠RST . . . . add 12, show units

The measure of angle RST is 120 degrees.

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Additional comment

Note that we don't actually need to know the value of x (18) in this problem. We only need to know the value of 6x.