m<1=2x°,m<2=(x-5)°,and m<3=100°.use an equation to find the measures of<1 and <2.
To find the measures of ∠1 and ∠2, we can use the fact that the three angles of a triangle add up to 180°. So, we'll write an equation using this information.
The measure of ∠1 is given as m∠1 = 2x°.
The measure of ∠2 is given as m∠2 = (x - 5)°.
The measure of ∠3 is given as m∠3 = 100°.
Using the fact that the sum of the three angles in a triangle is 180°, we have the equation:
m∠1 + m∠2 + m∠3 = 180°
Substituting the given values, we have:
2x + (x - 5) + 100 = 180
Simplifying the equation, we have:
2x + x - 5 + 100 = 180
Combining like terms, we have:
3x + 95 = 180
Subtracting 95 from both sides of the equation, we have:
3x = 180 - 95
Simplifying, we have:
3x = 85
Dividing both sides of the equation by 3, we have:
x = 85/3
Therefore, the value of x is x = 85/3.
Now we can find the measures of ∠1 and ∠2 by substituting the value of x into their respective equations:
m∠1 = 2(85/3) = 170/3 ≈ 56.67°
m∠2 = (85/3 - 5) = 70/3 ≈ 23.33°
Hence, the measures of ∠1 and ∠2 are approximately 56.67° and 23.33° respectively.