Given: triangle ABC ~ triangle PQR, m<A = 75 degrees, m<P = (5x + 7y) degrees, m<R = (3x + 4y) degrees, and m<B =( 2x + 9y) degrees. FInd m<R.
Thanks
very similar to the one I did for you yesterday.
draw the two triangles and fill in the information.
5x + 7y = 75 ---- equation #1
In triangle AC
angle C = 180 - 75 - 2x - 9y
= 105 - 2x - 9y
3x+4y = 105 - 2x - 9y
5x + 13y = 105 --- #2
subtract #2 - #1
6y = 30
y = 5
back into #1
5x + 35 = 75
5x = 40
x=8
so if x=8 and y=5
angle R = 3x+4y = 24+20 = 44°
check: 5x + 7y should be 75
5(8) + 7(5) = 75 , yeahhh
Okay, I get it now:)...thanks.
To find the measure of angle R (m<R), we can use the fact that corresponding angles in similar triangles are equal.
Given that triangle ABC is similar to triangle PQR, we can equate the corresponding angles:
m<A = m<P
75 = 5x + 7y [Equation 1]
Similarly, we can equate the angles B and Q:
m<B = m<Q
2x + 9y = ? [Equation 2]
Since we want to find m<R, we need to focus on the angles A and P.
To isolate x, we will solve Equation 1 for x:
75 = 5x + 7y
5x = 75 - 7y
x = (75 - 7y)/5 [Equation 3]
Now we substitute the value of x from Equation 3 into Equation 2 to solve for y:
2x + 9y = ?
2((75 - 7y)/5) + 9y = ?
(150 - 14y)/5 + 9y = ?
150 - 14y + 45y = ?*5
150 + 31y = ?*5
31y = ?*5 - 150
31y = ? - 150
y = (?-150)/31 [Equation 4]
Now that we have the value of y, we can substitute it back into Equation 3 to find the value of x:
x = (75 - 7y)/5
x = (75 - 7((?-150)/31))/5
x = (75 + 7(150/31))/5
x = (75 + 1050/31)/5
x = 225/31
Now that we have the values of x and y, we can substitute them into the equation for angle R:
m<R = 3x + 4y
m<R = 3(225/31) + 4((?-150)/31)
m<R = 675/31 + 4((?-150)/31)
m<R = (675 + 4(?-150))/31
m<R = (675 + 4? - 600)/31
m<R = (75 + 4?)/31
Therefore, the measure of angle R (m<R) is (75 + 4?)/31.