Chapter 2.7, Problem 20PSD

To determine

To calculate : All the possible values of x are to be calculated

Answer to Problem 20PSD

All the possible values of x are $({60}^0,{90}^0)$

Explanation of Solution

Given information : The following two statements are given

The angle must have a complement

Three fourths of the supplement of the angle must have a complement

Formula used : we add linearly to find values of x

Calculation : let us assume that the angle is x

Hence, we try to solve the first statement. We get

  $0^0<({90}^0-x)<{90}^0\to x\in (0,{90}^0)$

Now, we try to solve the second statement

  $0^0<\frac{3}{4}({180}^0-x)<{90}^0\to x\in ({60}^0,{180}^0)$

Now, we need an intersection of the two statements

Thus, final value of x

  $x\in (0,{90}^0)\cap ({60}^0,{180}^0)\to ({60}^0,{90}^0)$

Hence, the final answer is calculated