SAT Math: Geometry version 5

Lines and Angles


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In the figure shown above, four line segments join at a single point to form four angles.  What is the value of a?

A. 10
B. 18
C. 20
D. 35
E. 40

Knowsys Method

Read the question carefully.  Make note that the figure is not drawn to scale, so the sizes of the angles in the picture do not reflect their true measurements.

Identify the bottom line.  a = ?

Assess your options.  Visualize the point in the center as the center of a circle.  The number of degrees around the center point is 360, just like the number of degrees around the center of a circle.  That means that all of these angle measurements should add together to equal 360 degrees.  If you set that up as an equation, then you can solve for a.

Attack the problem.  Set up your equation and find the value of a.

2a + 4a + 5a + 7a = 360
                       18a = 360
                       ÷18    ÷18
                           a = 20

Loop back. Did you find the value of a?  Yes.  All that is left is to select the letter of the correct answer.
The correct answer is (C).

This is a medium level question.