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:

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

9)  2x - 9 < 7

Add 9 to both sides.

2x < 7 + 9

Simplify.

2x < 16

Divide both sides by 2.

x < 8

10)  Go through each answer choice & check.

a)  4n + 11 > -9

Subtract 11 from both sides.

4n > -9 - 11

Simplify.

4n > -20

Divide both sides by 4.

n > -5

(a) is incorrect.

b)  4n + 11 < -9

Subtract 11 from both sides.

4n < -9 - 11

Simplify.

4n < -20

Divide both sides by 4.

n < 5

(b) is incorrect

c)  -4n + 11 <-9

Subtract 11 from both sides.

-4n < -9 - 11

Simplify.

-4n < -20

Divide both sides by -4.

n > 5

(c) is incorrect

d)  -4n + 11 > -9

Subtract 11 from both sides.

-4n > -9 - 11

Simplify.

-4n > -20

Divide both sides by -4.

n < 5

(d) is correct

~Hope I helped!~