All SAT Math Resources
Example Questions
Example Question #6 :Other Polygons
In triangle美国广播公司, the measure of angleA= 70 degrees, the measure of angleB=xdegrees, and the measure of angleC=ydegrees. What is the value ofyin terms ofx?
110 –x
x– 70
110 +x
70 –x
70 +x
110 –x
Since the three angles of a triangle sum to 180, we know that 70 +x+y= 180。两边同时减去70,看看x+y= 110. Subtractxfrom both sides and see thaty= 110 –x.
Example Question #7 :Other Polygons
What is the measure, in degrees, of each interior angle of a regular convex polygon that has twelve sides?
120
135
180
175
150
150
The sum of the interior angles, in degrees, of a regular polygon is given by the formula 180(n –2), wheren是the number of sides. The problem concerns a polygon with twelve sides, so we will letn= 12. The sum of the interior angles in this polygon would be 180(12 – 2) = 180(10) = 1800.
Because the polygon is regular (meaning its sides are all congruent), all of the angles have the same measure. Thus, if we divide the sum of the measures of the angles by the number of sides, we will have the measure of each interior angle. In short, we need to divide 1800 by 12, which gives us 150.
The answer is 150.
Example Question #8 :Other Polygons
In the figure above, polygonABDFHGECis a regular octagon. What is the measure, in degrees, of angleFHI?
50
40
30
45
60
45
AngleFHI是the supplement of angleFHG, which is an interior angle in the octagon. When two angles are supplementary, their sum is equal to 180 degrees. If we can find the measure of each interior angle in the octagon, then we can find the supplement of angleFHG, which will give us the measure of angleFHI.
The sum of the interior angles in a regular polygon is given by the formula 180(n –2), wheren是the number of sides in the polygon. An octagon has eight sides, so the sum of the angles of the octagon is 180(8 – 2) = 180(6) = 1080 degrees. Because the octagon is regular, all of its sides and angles are congruent. Thus, the measure of each angle is equal to the sum of its angles divided by 8. Therefore, each angle in the polygon has a measure of 1080/8 = 135 degrees. This means that angleFHGhas a measure of 135 degrees.
Now that we know the measure of angleFHG, we can find the measure ofFHI. The sum of the measures ofFHGandFHI必须是180度,因为两个角度形成一个吗line and are supplementary. We can write the following equation:
Measure ofFHG+ measure ofFHI= 180
135 + measure ofFHI= 180
Subtract 135 from both sides.
Measure ofFHI= 45 degrees.
The answer is 45.
Example Question #9 :Other Polygons
What is the measure of each angle in a regular octagon?
An octagon contains six triangles, or 1080 degrees. This means with 8 angles, each angle is 135 degrees.
Example Question #10 :Other Polygons
What is the measure of each central angle of an octagon?
There are 360 degrees and 8 angles, so dividing leaves 45 degrees per angle.
Example Question #1 :How To Find An Angle In A Polygon
什么是平均(算术平均值)的15terior angles of a quadrilateral, pentagon, and hexagon?
The 4 angles of a quadrilateral add to 360
The 5 angles of a pentagon add to 540
The 6 angles of a hexagon add to 720
Example Question #2 :How To Find An Angle In A Polygon
Find the sum of the interior angles in a nonagon.
To solve, simply use the formula for the total degrees in a polygon, where n is the number of vertices.
In this particular case, a nonagon is a shape with nine sides and thus nine vertices.
Thus,
Example Question #3 :How To Find An Angle In A Polygon
Which of the followingcannotbe the measure of an exterior angle of a regular polygon?
If one exterior angle is taken at each vertex of any convex polygon, the sum of their measures is. In a regular polygon - one with congruent sides and congruent interior angles, each exterior angle is congruent to one another. If the polygon hassides, each exterior angle has measure.
Given the common measure,
Multiplying both sides by:
and
Sinceis equal to a number of sides, it is a whole number. Thus, we are looking for a value ofwhich, when we divide 360 by it, yields a non-whole result. We see that是the correct choice, since'
A quick check confirms that 360 divided by 8, 10, 12, or 15 yields a whole result.
Example Question #11 :How To Find An Angle In A Polygon
To the nearest whole degree, give the measure of each interior angle of a regular polygon with 17 sides.
The measure of each interior angle of an-sided polygon can be calculated using the formula
Setting:
The correct choice is therefore.
Example Question #12 :How To Find An Angle In A Polygon
Each interior angle of a regular polygon has measure. How many sides does the polygon have?
The easiest way to work this is arguably to examine the exterior angles, each of which forms a linear pair with an interior angle. If an interior angle measures, then each exterior angle, which is supplementary to an interior angle, measures
The measures of the exterior angles of a polygon, one per vertex, total; in a regular polygon, they are congruent, so if there aresuch angles, each measures. Since the number of vertices is equal to the number of sides, if we set this equal toand solve for, we will find the number of sides.
Multiply both sides by:
The polygon has 72 vertices and, thus, 72 sides.
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