Acute △ABC with angles α, β, and γ is inscribed in a circle. Tangents to the circle at points A, B, and C intersect in points M, N, and P. Find measures of angles of the △MNP.

The measures of angles of triangle MNP are

Step-by-step explanation:

The picture of the question in the attached figure

step 1

Find the measure of arcs AB, BC and AC

we know that

The inscribed angle is half that of the arc it comprises.

so

step 2

Find the measure of angle M

we know that

The measurement of the outer angle is the semi-difference of the arcs it encompasses.

substitute

step 3   

Find the measure of angle N

we know that

The measurement of the outer angle is the semi-difference of the arcs it encompasses.

substitute

step 4    

Find the measure of angle P

we know that

The measurement of the outer angle is the semi-difference of the arcs it encompasses.

substitute

b. 1.25 hr

step-by-step explanation:

if you have a constant speed of 60 mph, then you have a ratio between 60 mi. to 1 hr. dividing both sides by 60 we get the ratio

1 mi. to

then mult. both sides by 75 we get the ratio

75 mi. to

simplifying we get

75 mi. to

or 1.25 hr.