Question

lines, angles, and triangles practice set
directions: keep a calculator handy as you work through this practice set, but reserve it for those questions that
have a calculator icon next to them—and even on those questions, use it only if you really need it. questions without
the icon are intended to be done without a calculator, to help you prepare for the no - calculator section of the sat.

1. in the figure above, ( d = 105 ). if ( a = 2c ), what is the

value of ( a + b )?
a) 105
b) 120
c) 130
d) 145

1. in the given figure, lines ( a ), ( b ), and ( c ) intersect at one

point. what is the value of ( x )?
a) 33
b) 43
c) 57
d) 90

1. in the given figure, ( ab ) and ( de ) are parallel. what is

the length of ( ac )?
a) ( 2sqrt{181} )
b) 36
c) 54
d) ( 4sqrt{181} )

1. what is the value of ( c ) if the number of radians in a

630 - degree angle can be written as ( cpi ), where ( c ) is a
constant?
a) ( \frac{1}{6} )
b) ( \frac{5}{6} )
c) ( \frac{3}{2} )
d) ( \frac{7}{2} )

Explanation:

Step1: Use the exterior angle theorem

The exterior angle theorem states that \(d=a + c\). Given \(d = 105\), so \(a + c=105\). Also given \(a = 2c\). Substitute \(a = 2c\) into \(a + c=105\), we get \(2c + c=105\), which simplifies to \(3c=105\). Solving for \(c\), we have \(c = 35\). Then \(a=2c = 70\).

Step2: Use the linear - pair relationship

We know that \(b + c=180\) (linear - pair of angles). Since \(c = 35\), then \(b=180 - c=145\).

Step3: Calculate \(a + b\)

Now, \(a + b=70+145 = 145\).

Answer:

D. 145