All High School Math Resources
Example Questions
Example Question #2 : How To Find An Angle Of A Line
Give another name for .
Since the angle is called , it has vertex - the middle letter is always the vertex - and it is the union of rays and . Another name for is , since is also on that ray, so the angle can be said to be the union of and ; this makes a valid name for the angle.
and are not valid, since the middle letter is not vertex . is not valid, since and are on the same side of the angle. is not valid; an angle can be named using only its vertex only if it is the only angle in the diagram with that vertex, and that is not the case here.
Example Question #1162 : High School Math
Coresponding angles can be found when a line crosses two parallel lines. Angles 10 and 14 are equal, because corresponding angles are equal. Angles 14 and 13 are supplementary because together they form a straight line. If angles 10 and 14 are equal, then angles 10 and 13 must be supplementary as well.
Example Question #1 : Geometry
Two pairs of parallel lines intersect:
If A = 135o, what is 2*|B-C| = ?
170°
160°
150°
180°
140°
180°
By properties of parallel lines A+B = 180o, B = 45o, C = A = 135o, so 2*|B-C| = 2* |45-135| = 180o
Example Question #1 : Geometry
Two angles are supplementary and have a ratio of 1:4. What is the size of the smaller angle?
Since the angles are supplementary, their sum is 180 degrees. Because they are in a ratio of 1:4, the following expression could be written:
Example Question #2 : Geometry
Lines and are parallel. , , is a right triangle, and has a length of 10. What is the length of
Not enough information.
Since we know opposite angles are equal, it follows that angle and .
Imagine a parallel line passing through point . The imaginary line would make opposite angles with & , the sum of which would equal . Therefore, .
Example Question #3 : Geometry
If measures , which of the following is equivalent to the measure of the supplement of ?
When the measure of an angle is added to the measure of its supplement, the result is always 180 degrees. Put differently, two angles are said to be supplementary if the sum of their measures is 180 degrees. For example, two angles whose measures are 50 degrees and 130 degrees are supplementary, because the sum of 50 and 130 degrees is 180 degrees. We can thus write the following equation:
Subtract 40 from both sides.
Add to both sides.
The answer is .
Example Question #781 : New Sat
In the following diagram, lines and are parallel to each other. What is the value for ?
It cannot be determined
When two parallel lines are intersected by another line, the sum of the measures of the interior angles on the same side of the line is 180°. Therefore, the sum of the angle that is labeled as 100° and angle y is 180°. As a result, angle y is 80°.
Another property of two parallel lines that are intersected by a third line is that the corresponding angles are congruent. So, the measurement of angle x is equal to the measurement of angle y, which is 80°.
Example Question #511 : Plane Geometry
The angles are alternate exterior angles and are, therefore, equal.
Example Question #183 : Coordinate Geometry
The measure of the supplement of angle A is 40 degrees larger than twice the measure of the complement of angle A. What is the sum, in degrees, of the measures of the supplement and complement of angle A?
190
90
50
140
40
190
Let A represent the measure, in degrees, of angle A. By definition, the sum of the measures of A and its complement is 90 degrees. We can write the following equation to determine an expression for the measure of the complement of angle A.
A + measure of complement of A = 90
Subtract A from both sides.
measure of complement of A = 90 – A
Similarly, because the sum of the measures of angle A and its supplement is 180 degrees, we can represent the measure of the supplement of A as 180 – A.
The problem states that the measure of the supplement of A is 40 degrees larger than twice the measure of the complement of A. We can write this as 2(90-A) + 40.
Next, we must set the two expressions 180 – A and 2(90 – A) + 40 equal to one another and solve for A:
180 – A = 2(90 – A) + 40
Distribute the 2:
180 - A = 180 – 2A + 40
Add 2A to both sides:
180 + A = 180 + 40
Subtract 180 from both sides:
A = 40
Therefore the measure of angle A is 40 degrees.
The question asks us to find the sum of the measures of the supplement and complement of A. The measure of the supplement of A is 180 – A = 180 – 40 = 140 degrees. Similarly, the measure of the complement of A is 90 – 40 = 50 degrees.
The sum of these two is 140 + 50 = 190 degrees.
Example Question #2 : How To Find An Angle Of A Line
Lines A and B in the diagram below are parallel. The triangle at the bottom of the figure is an isosceles triangle.
What is the degree measure of angle ?
Since A and B are parallel, and the triangle is isosceles, we can use the supplementary rule for the two angles, and which will sum up to . Setting up an algebraic equation for this, we get . Solving for , we get . With this, we can get either (for the smaller angle) or (for the larger angle - must then use supplementary rule again for inner smaller angle). Either way, we find that the inner angles at the top are 80 degrees each. Since the sum of the angles within a triangle must equal 180, we can set up the equation as
degrees.
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