Answer:
The two angles below are complementary. m∠GHI=x. What is x?
[Figure 1]
Candace is puzzled. Are you? Using equations and geometry can help you figure this one out. Pay attention and you will learn all that you need to know from this Concept.
Explanation:
Let's think about angle pairs. There are different types of angle pairs.
Supplementary angles are two angles that form a straight line, and their sum is always 180∘.
Complementary angles together form a right angle and have a sum of 90∘.
Adjacent angles are next to each other. When they form a line, their sum is 180∘.
Vertical angles are directly opposite each other. They are equal.
Take a look at this situation involving angle pairs.
Fill in the figure below with the angle measures for all of the angles shown.
[Figure 2]
First, notice that we only have one angle to go on. This angle measures 70 degrees. However, that is enough information to figure out all of the other angles in this diagram. We can use the information that we know about angles to figure the measures of these angles out.
Let’s begin with adjacent angles. Angle b is adjacent to the 70 degree angle. Since we know that adjacent angles form a straight line, the sum of the two angles is 180∘.
We can write this equation.
180=70+b
We know that b is equal to 110∘.
Next, we can work on the vertical angles. Angle c is vertical with angle b. Vertical angles have the same measure, so the measure of angle c is also 110∘.
Angle a is vertical with the 70∘ given angle, we know that this one is also 70∘.
Using our known information, we have figured out the measures of all of the missing angles.
Find the measure of an angle that forms a supplementary angle with ∠MRS if m∠MRS is:
Example A
61∘
Solution: 119∘
Example B
40∘
Solution: 140∘
Example C
121∘
Solution: 59∘
Now let's go back to the dilemma from the beginning of the Concept.
[Figure 3]
If the two angles are complementary, then we know that the sum of the two angles is 90 degrees.
Let's write an equation to show that.
x+34=90
Now we can solve for x.
x=90−34
x=56∘