Question

Given that A, O & B lie on a straight line segment, evaluate obtuse ∠AOC.

The diagram is not drawn to scale. < AOC=

Answer 1

∠ AOC = 124°

Explanation:

the 3 angles lie on a straight line and sum to 180°

sum the 3 angles and equate to 180

3x + 94 + x + 30 + 2x - 4 = 180

6x + 120 = 180 ( subtract 120 from both sides )

6x = 60 ( divide both sides by 6 )

x = 10

Then

∠ AOC = 3x + 94 = 3(10) + 94 = 30 + 94 = 124°

Answer 2

∠AOC is 124 degrees.

To find the measure of angle AOC (∠AOC), you can use the fact that the sum of angles on a straight line is 180 degrees.

Since A, O, and B lie on a straight line segment, the sum of the three angles AOC, COD, and DOB is equal to 180 degrees.

∠AOC+∠COD+∠DOB=180

Now, substitute the given expressions for the angles:

(3X+94)+(X+30)+(2X−4)=180

Combine like terms:

6X+120=180

Subtract 120 from both sides:

6X=60

Divide by 6:

X=10

Now that you know the value of X, you can substitute it back into the expression for ∠AOC:

∠AOC=3X+94

∠AOC=3(10)+94

∠AOC=30+94

∠AOC=124

So, ∠AOC is 124 degrees.