Find the measure. M<1,m<2,m<3

C) m∠1 = 45°, m∠2 = 76°, m∠3 = 80°

Step-by-step explanation:

In the given figure. There are two triangles. We have to use the concept of the sum of interior angles of a triangle is 180°.

So,

m∠2 + 45° + 59° = 180

m∠2 + 104° = 180°

m∠2 = 180° -104°

m∠2 = 76°

m∠1 and 45° are the opposite angles. When two lines are intersection each there, then the opposite angles must be equal.

Therefore, m∠1 = 45°

m∠1 + m∠3 + 55° = 180

45° + m∠3 + 55° = 180°

m∠3 + 100° = 180°

m∠3 = 180° -100°

m∠3 = 80°

Therefore, m∠1 = 45°, m∠2 = 76°, m∠3 = 80°

Answer is C) m∠1 = 45°, m∠2 = 76°, m∠3 = 80°

answer: 0.64

step-by-step explanation:

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240