Answer:
22
Step-by-step explanation:
m1 + m2 = 180
3x - 17 + 5x + 21 = 180
3x + 5x + 21 - 17 = 180
8x + 4 = 180
8x = 180 - 4
8x = 176
x = 176 / 8
x = 22
Answer:
a = <u>76°</u>
b = <u>124°</u>
Step-by-step explanation:
Since the lines are parallel, we can prove that the smaller triangle's missing angle (shares a line with ∠b) is 56°.
180-56=124°
∠b=124°
Now to find Angle A:
180-56-48=
124-48=
76°
∠a=76°
Answer:
3/5
Step-by-step explanation:
Given
Number of women in the math class = 7
Number of men = 9
Total = 9 + 7 = 15
Probability of selecting a man at random to come to the board and show solution to a math problem
= number of men/total number of persons in the class
That’s
9/15
Divide both the numerator and denominator by 3
3/5
The probability of picking a man student is 3/5
Use the cosine law to find the length of side c:
![\begin{gathered} c^2=1^2+9^2-2(1)(9)\cos 60 \\ c^2=1+81-18\cos 60 \\ c^2=82-18\cos 60 \\ c^2=82-9 \\ c^2=73 \\ c=\sqrt[]{73} \\ c\approx8.54 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20c%5E2%3D1%5E2%2B9%5E2-2%281%29%289%29%5Ccos%2060%20%5C%5C%20c%5E2%3D1%2B81-18%5Ccos%2060%20%5C%5C%20c%5E2%3D82-18%5Ccos%2060%20%5C%5C%20c%5E2%3D82-9%20%5C%5C%20c%5E2%3D73%20%5C%5C%20c%3D%5Csqrt%5B%5D%7B73%7D%20%5C%5C%20c%5Capprox8.54%20%5Cend%7Bgathered%7D)
Use the cosine law to find the measure of angles A or B:
![\begin{gathered} \\ \frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c} \\ \\ To\text{ find angle A:} \\ \frac{\sin A}{a}=\frac{\sin C}{c} \\ \\ \frac{\sin A}{1}=\frac{\sin 60}{\sqrt[]{73}} \\ \\ \sin A=\frac{\sin 60}{\sqrt[]{73}} \\ \\ A=\sin ^{-1}(\frac{\sin60}{\sqrt[]{73}}) \\ \\ A\approx5.82º \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%20%5C%5C%20%5Cfrac%7B%5Csin%20A%7D%7Ba%7D%3D%5Cfrac%7B%5Csin%20B%7D%7Bb%7D%3D%5Cfrac%7B%5Csin%20C%7D%7Bc%7D%20%5C%5C%20%20%5C%5C%20To%5Ctext%7B%20find%20angle%20A%3A%7D%20%5C%5C%20%5Cfrac%7B%5Csin%20A%7D%7Ba%7D%3D%5Cfrac%7B%5Csin%20C%7D%7Bc%7D%20%5C%5C%20%20%5C%5C%20%5Cfrac%7B%5Csin%20A%7D%7B1%7D%3D%5Cfrac%7B%5Csin%2060%7D%7B%5Csqrt%5B%5D%7B73%7D%7D%20%5C%5C%20%20%5C%5C%20%5Csin%20A%3D%5Cfrac%7B%5Csin%2060%7D%7B%5Csqrt%5B%5D%7B73%7D%7D%20%5C%5C%20%20%5C%5C%20A%3D%5Csin%20%5E%7B-1%7D%28%5Cfrac%7B%5Csin60%7D%7B%5Csqrt%5B%5D%7B73%7D%7D%29%20%5C%5C%20%20%5C%5C%20A%5Capprox5.82%C2%BA%20%5Cend%7Bgathered%7D)
