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ACT Math: Geometry

SAT Question of the Day

The SAT question of the day is an Identifying Sentence Errors Question that has already been addressed on this blog: click here to see an explanation.

ACT Question of the Day

The ACT question of the day is a geometry question that tests you knowledge of triangles.  

The question gives you a diagram of a triangle labeled LMN.  You know that angles L is 22 degrees.  The question also tells you that this is an isosceles triangle that is drawn to scale.  You must find the measure of angle N

What do you know about isosceles triangles?  Not only do they always have two sides that are the same length, but they also have two angles that are the same length.  Look again at the diagram of the triangle.  You know the triangle is drawn to scale.  Does angle N  look like it would match angle L?  No!  Angle L is too small.  That means that angle N and angle M must be the same size.  Check the diagram.  They look the same size.

You do not know the value of angle N or the value of angle M, but you do know something else about all triangles:  the three angles must add up to 180 degrees.

L + M + N = 180.          Plug in 22 for L.  

22 + M + N = 180.          M and N have to be the same.  You can put an N instead of an M.

22 + N + N = 180          Combine like terms.

22 + 2N = 180          Isolate the variable.

2N = 158

N = 79

The correct answer is (D).

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