Question 148651
1. In the convex quadrilateral ABCD if ,angel a is congruent to angel d  and, measure of angel b=110 degrees and measure of c=60  find a .

 a.95 ° 
 b.170° 
 c.190° 
 d.360° 


add b and c: 110 +60=170
subtract that from 360, since the degrees of a quad is 360:
360-170=190
Divide that by two since a and d are congruent
190/2=95


So the answer is a)95 degrees.
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2. Suppose that the interior angles of a convex pentagon are five consecutive numbers. What is the measure of the largest angle?

 a.105° 
 b.106° 
 c.109° 
 d.110° 


Since these five numbers are consecutive, then this can be written as:
x+(x+1)+(x+2)+(x+3)+(x+4)
Set that equal to 540, since the angles of pentagon add up to 540:
x+(x+1)+(x+2)+(x+3)+(x+4)=540
Combine like terms:
5x+10=540
5x=530
x=106


Largest angle=x+4 or 106+4
Largest angle=110 degrees


So the answer is d)110 degrees.
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3. If five of the exterior angles of a convex hexagon measure 55°, 60°, 63°, 70°, and 81°, find the measure of the sixth exterior angle.

 a.31° 
 b.60° 
 c.120° 
 d.391° 


First find the measure of the first five interior angles, which can be found by subtracting the exterior angle from 180.  You get:
125, 120, 117, 110, and 99.
Now add them together:
125+120+117+110+99=571
Now subtract that from 720, since the degrees of a hexagon add up to 720.
720-571=149
That is the sixth interior angle.  Now subtract that from 180 to get the exterior:
180-149=31


So the answer is a)31 degrees.
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4.  How many sides would a regular polygon have if each interior angle measures 162°?

 a.10 
 b.12 
 c.18 
 d.20


Use the formula [180(n-2)]/n to get the measure of an interior angle of a regular polygon.  If each angle is 162, then set it equal to that:


[180(n-2)]/n=162
Now multiply both sides by n
180(n-2)=162n

Distribute 180 to n-2
180n-360=162n
Subtract 180n from both sides
-360=-18n
Divide both sides by -18
20=n


So the answer is d)20 sides.
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5. How many angles would a regular polygon have if each exterior angle measures 5°?

 a.36 
 b.37 
 c.72 
 d.74 


First get the measure of the interiors by subtracting the exterior from 180:
180-5=175.
Then use [180(n-2)]/n as in the last question, but this time set it equal to 175:


[180(n-2)]/n=175

Now multiply both sides by n
180(n-2)=175n

Distribute 180 to n-2
180n-360=175n
Subtract 180n from both sides
-360=-5n
Divide both sides by -5
72=n

So the answer is c)72 angles.