Use what you know about the sum of the angles of a triangle to find m

Angle ABC is 22 degrees

Angle BAC is 68 degrees

Work Shown:

Because there are just 3 points, we can refer to "angle BAC" as "angle A" and "angle ABC" as "angle B". Focus on the middle letter of each three-letter sequence.

The three angles A, B, C add up to 180 degrees. This is true for any triangle.

A+B+C = 180

(6x+8) + (2x+2) + 90 = 180 ... substitution

6x+8 + 2x+2 + 90 = 180

8x+100 = 180

8x+100-100 = 180-100 ... subtract 100 from both sides

8x = 80

8x/8 = 80/8 ... divide both sides by 8

x = 10

If x = 10, then angle BAC is

angle BAC = 6x+8

angle BAC = 6*10+8

angle BAC = 60+8

angle BAC = 68

Use x = 10 to find angle ABC as well

angle ABC = 2x+2

angle ABC = 2*10+2

angle ABC = 20+2

angle ABC = 22

The three angles of this triangle are A = 68, B = 22, C = 90

As a check, the three angles must add to 180

A+B+C = 180

68+22+90 = 180

180 = 180

Answers are confirmed

Another thing to notice is that A+B = 90 meaning that A and B are complementary angles. A+B = 68+22 = 90.

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.

step-by-step explanation: