Angle pairs and one step equations :
Vertical angles are the opposite angles formed by two intersecting lines. Vertical angles are congruent because the angles have the same measure.
Adjacent angles are pairs of angles that share a vertex and one side but do not overlap.
Complementary angles are two angles whose measures have a sum of 90°.
Supplementary angles are two angles whose measures have a sum of 180°. We discovered in the Explore Activity that adjacent angles formed by two intersecting lines are supplementary.
Example 1 :
Look at the diagram given below and answer the question.
A. Name a pair of vertical angles :
Vertical angles are opposite angles formed by intersecting lines.
<AFB and <DFE are vertical angles.
B. Name a pair of adjacent angles :
Adjacent angles share a vertex and a side but do not overlap.
<AFB and <BFD are adjacent angles.
C. Name a pair of supplementary angles :
Adjacent angles formed by intersecting lines are supplementary.
<AFB and <BFD are supplementary angles.
D. Name two pairs of supplementary angles that include <DFE :
Any angle that forms a line with <DFE is a supplementary angle to <DFE.
<DFE and <EFA are supplementary angles, as are <DFE and <DFB.
E. Find the measure of angle <AFB :
Use the fact that <AFB and <BFD in the diagram are supplementary angles to find m<AFB.
<AFB + <BFD = 180°
From the given diagram, we have <AFD = x and also m<BFD = 50° + 90° = 140°
x + 140° = 180°
Subtract 140° from both sides.
(x + 140°) - 140° = 180° - 140°
x = 40°
The measure of m<AFB is 40°
Example 2 :
Find the value of "x" in the diagram given below.
From the picture above, it is very clear (x+7)° and 100° are vertical angles and also they are congruent.
So, we have
x + 7 = 100
Subtract 7 from both sides
(x + 7) - 7 = 100 - 7
x = 93
Hence the value of "x" is 93.
After having gone through the stuff given above, we hope that the students would have understood "One step equations on angle pairs".
Apart from the stuff given above, if you want to know more about "Angle pairs and one step equations", please click here
Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.
APTITUDE TESTS ONLINE
ACT MATH ONLINE TEST
TRANSFORMATIONS OF FUNCTIONS
ORDER OF OPERATIONS
MATH FOR KIDS
HCF and LCM word problems
Word problems on quadratic equations
Word problems on comparing rates
Ratio and proportion word problems
Converting repeating decimals in to fractions