Answer:
Step-by-step explanation:
<u>Angles and Lines</u>
It's convenient to recall two basic principles of angles:
The sum of internal angles in a triangle is 180°
Two linear angles are supplementary, i.e. they sum 180°.
Angles ABC and CBD are linear. Since we know the measure of angle CBD, thus the measure of angle ABC is 180°-6x.
Now focus on the triangle. The sum of its internal angles is:
x + 40 + 3x + 10 + 180 - 6x = 180
Simplifying:
-2x + 230 = 180
Subtracting 230:
-2x = -50
Dividing by -2:
x = -50 / (-2) = 25
x = 25°
Now find the measure of angle CAB
Answer:
<em>Jessica is currently 3 years old and her father is 27 years old.</em>
Step-by-step explanation:
<u>System of Equations</u>
Let's call:
x = Jessica's age
y = Jessica's father's age.
There are two conditions:
1: Jessica's father is 24 years older than her or, equivalently:
y = x + 24
2: Three years from now, he will have five times her age.
Three years from now, Jessica will have x+3 years, and her father will have y+3 years, thus:
y + 3 = 5( x + 3 )
Substituting the first condition into the second:
x + 24 + 3 = 5( x + 3 )
Operating:
x + 27 = 5x + 15
Subtracting x and 15:
27 - 15 = 5x - x
12 = 4x
Solving:
x = 12 / 4 = 3
x = 3
y = 3 + 24 = 27
y = 27
Jessica is currently 3 years old and her father is 27 years old.
Two hundred fifty point six hundred eleven