Question

1. (12) use the inch ruler below to measure the distance (in inches) between point p and line n. a. approximately 1\frac{1}{4} inches b. approximately 1\frac{3}{4} inches c. approximately \frac{3}{4} of an inch d. approximately 2 inches e. approximately 1 inch 13. (16) find the measures of the complement and the supplement of angle m∠ace = 71. a. complement: 64 supplement: 125 b. complement: 19 supplement: 109 c. complement: 23 supplement: 93 d. complement: 45 supplement: 45 e. none of the above 14. (16) find the measures of the complement and the supplement of angle m∠m=x + 45. a. complement: 45 supplement: 135 b. complement: 45 - x supplement: 135 - x c. complement: 90 - x supplement: 180 - x d. complement: x - 45 supplement: x - 135 e. complement: x + 45 supplement: x + 135

Explanation:

Step1: Measure distance in Q12

By observing the ruler, the distance from point $P$ to line $n$ is approximately $1\frac{1}{4}$ inches.

Step2: Find complement in Q13

The complement of an angle $\theta$ is $90 - \theta$. For $\angle ACE = 71$, the complement is $90 - 71=19$.

Step3: Find supplement in Q13

The supplement of an angle $\theta$ is $180 - \theta$. For $\angle ACE = 71$, the supplement is $180 - 71 = 109$.

Step4: Find complement in Q14

The complement of $\angle M=x + 45$ is $90-(x + 45)=45 - x$.

Step5: Find supplement in Q14

The supplement of $\angle M=x + 45$ is $180-(x + 45)=135 - x$.

Answer:

1. A. approximately $1\frac{1}{4}$ inches
2. B. complement: 19, supplement: 109
3. B. complement: $45 - x$, supplement: $135 - x$