Question

1. (4 - 40) review. geometry use the relationships in the diagrams below to write an equation and solve for x.

a.

b. 2x + 20° 3x + 20°

1. (4 - 43) review: geometry when she was younger, mary had to look up at a 68° angle to see into her father’s eyes whenever she was standing 15 inches away. how high above the flat ground were her father’s eyes if mary’s eyes were 32 inches above the ground? draw a sketch of this situation and use your trig table to help you solve.

Explanation:

Step1: Analyze part a

There is no variable $x$ in the right - triangle in part a, so we focus on part b. In part b, the sum of the angles around a point is $360^{\circ}$.

Step2: Write the equation

The sum of the angles $2x + 20^{\circ}+3x + 20^{\circ}+2x+x=360^{\circ}$.
Combining like - terms, we get $(2x+3x + 2x+x)+(20^{\circ}+20^{\circ})=360^{\circ}$, which simplifies to $8x + 40^{\circ}=360^{\circ}$.

Step3: Solve the equation for $x$

Subtract $40^{\circ}$ from both sides: $8x=360^{\circ}- 40^{\circ}=320^{\circ}$.
Then divide both sides by 8: $x=\frac{320^{\circ}}{8}=40^{\circ}$.

Answer:

$x = 40^{\circ}$