Answer:Substitute the given values in the Law of Sines and find that the measure is 24.72°
1. 
, then 
and triangles ADC and ACB are similar by AAA theorem.
2. The ratio of the corresponding sides of similar triangles is constant, so
.
3. Knowing lengths you could state that 
.
4. This ratio is equivalent to 
.
5. 
, then 
and triangles BDC and BCA are similar by AAA theorem.
6. The ratio of the corresponding sides of similar triangles is constant, so
.
7. Knowing lengths you could state that 
.
8. This ratio is equivalent to 
.
9. Now add results of parts 4 and 8:
.
10. c is common factor, then:
.
11. Since 
you have 
.
It's a complementary angle, so just solve for x and subtract the CBD from 90,
First, we have to solve for x.
2x + 14 + x + 7 = 90
Combine like terms
3x + 21 = 90
Balance, subtract 21 from each side.
3x = 69
Divide 3 from each side
x = 23.
So know that we know x is 23, we can go about it 2 ways, subtracting the other angle with 90 or just substituting the variable, I'd just substitute the variable for it so just do 23 + 7. That equals 30, angle ABC = 30.
Answer:
x=-4 y=-1
Step-by-step explanation:
Let's solve your system by substitution.
−3x−8y=20;y=5x+19
Rewrite equations:
y=5x+19;−3x−8y=20
Step: Solve y=5x+19for y:
y=5x+19
Step: Substitute5x+19foryin−3x−8y=20:
−3x−8y=20
−3x−8(5x+19)=20
−43x−152=20(Simplify both sides of the equation)
−43x−152+152=20+152(Add 152 to both sides)
−43x=172
−43x
−43
=
172
−43
(Divide both sides by -43)
x=−4
Step: Substitute−4forxiny=5x+19:
y=5x+19
y=(5)(−4)+19
y=−1(Simplify both sides of the equation)
Answer:
x=−4 and y=−1
It’s actually true!
^ ^ ^ ^
<—|——|——|——|——|—>
-2 -1 0 1 2
The 4 arrows above the number line represents the distance between 2 and -2 which is 4!
