Question

find m∠AOB:::::::::::::::::::::::::::

Answer 1

Answer:

in pic

Please thank at least 5 of my answers.

Answer 2

Given,

Refer figure.

To find,

m ∠AOB.

Solution,

In the given figure, three angles, ∠AOC, ∠AOB, and ∠BOC are there.

Further, the measures of these angles are given as follows.

∠AOC = 108°,

∠AOB = (3x + 4)°, and,

∠BOC = (8x - 28)°.

Now, from the figure, it can be seen that,

∠AOB + ∠BOC = ∠AOC     ...(1)

Substituting the given values in the above equation (1), we get,

(3x + 4) + (8x - 28) = 108

Simplifying,

11x - 24 = 108

⇒ 11x = 132

⇒ x = 12.

Now, the value of the required ∠AOB can be found by substituting the value of x in the given value of this angle. That is,

∠AOB = 3x + 4 = 3(12) + 4 = 36 + 4 = 40°.

⇒ ∠AOB = 40°.

Therefore, the measure of the ∠AOB is 40°.