Answer:
- m∠ABX = (12+4y)°
- equation: (12+4y) +y = 92
- m∠ABX = 76°
- m∠CBX = 16°
Step-by-step explanation:
The reason this is titled "Mathematical Connections" is because you're supposed to draw upon all of the things you have learned about angles and equations and put them together to solve this problem. No problem-specific teaching should be necessary.
__
The words and diagram tell you that ...
m∠ABX + m∠CBX = 92°
They also tell you that ...
m∠CBX = y°.
The words tell you that m∠ABX = 12° + 4(m∠CBX). Since m∠CBX = y°, this means ...
m∠ABX = (12 +4y)° . . . . . this expression fills the box on the diagram
__
So, we have expressions involving y for each of the parts of angle ABC. We can substitute those expressions into the angle sum equation to get
(12 +4y) + (y) = 92 . . . . . . dropping the degree symbol, using only numbers
__
Using what you know about algebra and 2-step equations, you can solve this to find the value of y.
5y +12 = 92 . . . . . simplify
5y = 80 . . . . . . . . subtract 12
y = 16 . . . . . . . . . . divide by 5
This value can be substituted back into the expressions for angle measure:
m∠CBX = y° = 16°
m∠ABX = (12+4y)° = (12 +4·16)° = 76°
