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Given the expression (11x - 1)º, (5x + 5), and (3x + 5)º, what is the measure of angle O?

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Final answer:

The measure of angle O, from the equation (11x - 1)˚ + (5x + 5) + (3x + 5)˚ = 180, we find that angle O measures 41°.

Step-by-step explanation:

Given the expressions (11x - 1)˚, (5x + 5), and (3x + 5)˚, we are looking for the measure of angle O.

In order to find angle O, we need to solve the equation (11x - 1)˚ + (5x + 5) + (3x + 5)˚ = 180° because the sum of the angles in a triangle is 180°.

We can simplify the equation by combining like terms and applying basic algebraic operations:

(11x - 1)˚ + 5x + 5 + (3x + 5)˚ = 180°

11x + 5x + 3x - 1 + 5 + 5 = 180°

19x + 9 = 180°

19x = 171°

x = 9°

Now, substitute the value of x back into the expressions to find the measures of the angles:

(11x - 1)˚ = (11(9) - 1)˚ = 98°

(5x + 5) = (5(9) + 5) = 50°

(3x + 5)˚ = (3(9) + 5)˚ = 41°

Therefore, the measure of angle O is 41°.

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