Find ratios

4. a string that is 75 inches long will be cut into two pieces in the ration of 4: 11. find the lengths
of the two pieces of string.

5. the ratio of two supplementary angles is 4: 1. find the measures of the two angles.

6. the ratio of the measures of the angles in a triangle is 3: 5-7. find the measure of each angle.

7. the ratio of the measure of the sides of a triangle is 5; 7: 8 and its perimeter is 40 inches. find
the measure of each side.

Step-by-step explanation:

4. 4+11=15

to find the length of The first piece

4/15*75=20

to find the length of the second one

11/15*75=55

5. 4+1=5

to find the length of the first one

4/5*180=144

to find the length of the second one

1/5*180=36

7. 5+7+8=20

to find the length of the first one

5/20*40=10

to find the length of the second one

7/20*40=14

to find the length of the third one

8/20*40=16

option a, c,d are correct.

step-by-step explanation:

from the given figure, it is given that z is equidistant from the sides of the triangle rst, then from triangle tzb and triangle szb, we have

tz=sz(given)

bz=zb(common)

therefore, by rhs rule,δtzb ≅δszb

by cpctc, sz≅tz

also, from δctz and δasz,

tz=sz(given)

∠tcz=∠saz(90°)

by rhs rule, δctz ≅ δasz, therefore by cpctc, ∠ctz≅∠asz

also,from δasz and δzsb,

zs=sz(common)

∠zbs=∠saz=90°

by rhs rule, δasz ≅δzsb, therefore, by cpctc, ∠asz≅∠zsb

hence, option a, c,d are correct.