The m<A is 10 more than 4 times its supplement. Find the m<A.
I don't understand how to solve this problem.. Thank You for your help.
let angle A be Ø
its supplement is 180-Ø
so Ø = 4(180-Ø) - 10
Ø = 720 - 4Ø - 10
5Ø = 710
Ø = 142
check:
if Ø = 142, then its supplement is 38
is 4x38 - 10 equal to 142 ???
Ya its correct
Thank You
Supplement = X DEG.
A = 4X + 10.
X + (4X + 10) = 180,
5X + 10 = 180,
5X = 180 - 10,
SX = 170,
X = 170 / 5 = 34.
A = 4*34 + 10 = 146 Deg.
To solve the problem, we will set up an equation based on the given information and then solve it algebraically.
Let's assign variables to the angles to make it easier to work with. Let m<A represent the measure of angle A. Since angle A has a supplement, let's assign m<B to represent the measure of angle B, which is the supplement of angle A.
According to the given information, "The m<A is 10 more than 4 times its supplement." We can write this statement as an equation:
m<A = 4m<B + 10
Now, let's substitute the measure of angle B in terms of its supplement into the equation. Recall that supplementary angles add up to 180 degrees, so:
m<B + m<A = 180
Rearranging this equation, we have:
m<B = 180 - m<A
Substituting this expression for m<B into the first equation, we get:
m<A = 4(180 - m<A) + 10
Now, we can solve this equation for m<A.
Simplifying the equation:
m<A = 720 - 4m<A + 10
Combining like terms:
m<A + 4m<A = 730
Simplifying further:
5m<A = 730
Finally, isolate m<A by dividing both sides of the equation by 5:
m<A = 730/5
m<A = 146
Therefore, the measure of angle A is 146 degrees.