Question

Line ac intersects line bd at point o. Line ac intersects line bd at point o. If m∠aod = (2x 12)° and m∠doc = (8x − 2)°, what is m∠aod?

Option 1: 134°
Option 2: 46°
Option 3: 28°
Option 4: 17°

Answer 1

The measure of angle AOD is approximately 16 and 2/3 degrees.

Step-by-step explanation:

To find the measure of angle AOD, we can set the two given expressions for the angle equal to each other:

(2x + 12)° = (8x - 2)°

Now, solve for x:

2x + 12 = 8x - 2

Subtract 2x from both sides

12 = 6x - 2

Add 2 to both sides:

14 = 6x

Divide by 6:

x = 14/6 = 7/3

Now, plug x back into one of the expressions to find the measure of angle AOD:

m∠aod = (2x + 12)°

m∠aod = (2(7/3) + 12)°

m∠aod = (14/3 + 12)°

m∠aod = (14/3 + 36/3)°

m∠aod = 50/3°

To convert to a mixed number, divide 50 by 3:

50 ÷ 3 = 16 remainder 2

So, the measure of angle AOD is approximately 16 and 2/3 degrees.