The measure of angle O = 75°
STEP - BY - STEP EXPLANATION
What to find?
The measure of angle O.
Given:
m
To determine the value of angle O, we will follow the steps below:
Step 1
Find the step of interior angle of a 5 - sided polygon using the formula below:
The sum of interior angle of an n-sided polygon = (n-2)180°
where n is the number of sides.
For a 5 - sided polygon, n= 5
Substitute n=5 into the formula and simplify.
The sum of interior angle = (5 - 2) 180°
= 3 x 180°
=540°
Step 2
Add all the angles given.
sum of the given angle = 116° + 112° + 132° + 105° =465°
Step 3
Subtract the resultant in step 2 from the resultant in step 1.
That is;
angle o = 540° - 465°
=75°
Therefore, the measure of angle O is 75°