Question

1. jie asked 90 students to choose 1 favorite fruit from 4 options. jie has begun to represent the results in the circle graph below. peaches were chosen as the favorite of 15 students. apples, bananas, and strawberries were each chosen as favorites by an equal number of the remaining students. what must be the measure of the central angle in the circle graph for bananas? favorite fruit peach 15 f. 100° g. 102° h. 105° j. 112.5° k. 115°

Explanation:

Step1: Calculate remaining students

$90 - 15=75$

Step2: Find number of students who chose bananas

Since apples, bananas and strawberries were chosen by equal - number of remaining students, $\frac{75}{3}=25$

Step3: Calculate proportion of students who chose bananas

The proportion of students who chose bananas out of the total 90 students is $\frac{25}{90}=\frac{5}{18}$

Step4: Calculate central angle for bananas

A full - circle is $360^{\circ}$. So the central angle for bananas is $\frac{5}{18}\times360^{\circ}=100^{\circ}$

Answer:

F. $100^{\circ}$