Question

Find the value or measure. Assume all lines that appear to be tangent are tangent.

m_OTS = 80^∘ , T = 154^∘ , O = 154^∘ , S = 30^∘ , 234^∘

a) 124^∘

b) 46^∘

c) 36^∘

d) 86^∘

Answer 1

The measure of angle TOS is 248 degrees.

Step-by-step explanation:

The angles in a triangle add up to 180 degrees. We are given the measures of m∡OTS, T, O, S, and we need to find the measure of angle TOS. Since TOS is an angle in triangle TOS, we can use the fact that the sum of the measures of the angles in a triangle is 180 degrees to find the value of angle TOS.

First, add up the known angle measures: 80^∘ + 154^∘ + 154^∘ + 30^∘ + 234^∘ = 652^∘.

Next, subtract the sum from 180 degrees to find the measure of angle TOS: 180^∘ - 652^∘ = -472^∘. However, angles can only be between 0 degrees and 360 degrees, so we need to find the positive equivalent of -472^∘ within this range. To do this, we can continuously add or subtract 360 degrees until we get a positive angle within the range. In this case, -472^∘ + 360^∘ = -112^∘. Since -112^∘ is still negative, we add another 360 degrees: -112^∘ + 360^∘ = 248^∘. Therefore, the measure of angle TOS is 248 degrees.