Chapter 1, Problem 35RP

a

To determine

To calculate: The Limitations on $m\angle Q$ are to be calculated

Answer to Problem 35RP

The upper and lower boundary limits of Q found are ${90}^o<m\angle Q<{180}^o$

Explanation of Solution

Given information: $\angle Q$is obtuse

Formula used: Obtuse angle restrictions used

Calculation: Using obtuse angle definition, we get :

  ${90}^o<\angle obtuse<{180}^o$

Now, we substitute the value of $\angle obtuse$ with $\angle Q$ ,

Thus we get :

  ${90}^o<m\angle Q<{180}^o$

b

To determine

To calculate: The restrictions on x are to be calculated

Answer to Problem 35RP

The limits of the x will be ${59}^o<x<{104}^o$

Explanation of Solution

Given information: $\angle Q$ is obtuse

  $m\angle Q={(2x-28)}^o$

Formula used: ${90}^o<m\angle Q<{180}^o$

Calculation: We use the two given equations :

  ${90}^o<m\angle Q<{180}^o$

  $m\angle Q={(2x-28)}^o$

Solving the above two equations, we get

  ${59}^o<x<{104}^o$