http://www.ck12.org Chapter 1. Basics of Geometry
Solution:Using the Angle Addition Postulate,m^6 QRT= 15 ◦+ 30 ◦= 45 ◦.
Example 10:What ism^6 LMNifm^6 LMO= 85 ◦andm^6 NMO= 53 ◦?
Solution: From the Angle Addition Postulate,m^6 LMO=m^6 NMO+m^6 LMN. Substituting in what we know,
85 ◦= 53 ◦+m^6 LMN, so 85◦− 53 ◦=m^6 LMNorm^6 LMN= 32 ◦.
Example 11:Algebra ConnectionIfm^6 ABD= 100 ◦, findxandm^6 ABCandm^6 CBD?
Solution:From the Angle Addition Postulate,m^6 ABD=m^6 ABC+m^6 CBD. Substitute in what you know and solve
the equation.
100 ◦= ( 4 x+ 2 )◦+( 3 x− 7 )◦
100 ◦= 7 x− 5 ◦
105 ◦= 7 x
15 ◦=xSo,m^6 ABC= 4 ( 15 ◦)+ 2 ◦= 62 ◦andm^6 CBD= 3 ( 15 ◦)− 7 ◦= 38 ◦.
Know What? RevisitedUsing a protractor, the measurement marked in the red triangle is 90◦, the measurement in
the green triangle is 45◦and the measurement in the blue square is 90◦.
All of the equal angles are marked in the picture below. All of the acute angles in the triangles are equal and all the
other angles are right, or 90◦.