Exercise 12 Page 550

Let's first find the measure of each angle. To determine the sum of the interior angles in a polygon, we use the formula 180^(∘)(n-2) where n is the number of sides. By equating the sum of the angles' expressions with 540^(∘), we can find the value of x.

(3x-26^(∘))+(2x+70^(∘))+(5x-10^(∘))+3x+(2x+56^(∘))=540^(∘)

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Solve for x

RemovePar

Remove parentheses

3x-26^(∘)+2x+70^(∘)+5x-10^(∘)+3x+2x+56^(∘)=540^(∘)

AddSubTerms

Add and subtract terms

15x+90^(∘)=540^(∘)

SubEqn

LHS-90^(∘)=RHS-90^(∘)

15x=450^(∘)

DivEqn

.LHS /15.=.RHS /15.

x=30^(∘)

When we know that x= 30^(∘) we can find the measure of each angle. 3( 30^(∘))-26^(∘)& = 64^(∘) 2( 30^(∘))+70^(∘)& = 130^(∘) 5( 30^(∘))-10^(∘)& = 140^(∘) 3( 30^(∘))& = 90^(∘) 2( 30^(∘))+56^(∘)& = 116^(∘) As we can see, 4 of 5 angles are greater than or equal to 90^(∘). Therefore, the probability of selecting an angle that is more than or equal to 90^(∘) must be 4 5.