in triangles PQR, m<P= 4/5(m<Q) and the measure of an exterior angle at R is 144. Find m<Q.
The exterior angle of a triangle is equal to the sum of the 2 interior and opposite angles.
so..
angle Q + 4/5 angle Q = 144 (multiply by 5)
5angle Q + 4angle Q = 720
9angle Q = 720
angle Q = 80
th for helping me this helped a lot ty ty ty ty ty ty ty ty.....
To find the measure of angle Q in triangle PQR, we can use the fact that the measure of an exterior angle of a triangle is equal to the sum of its two non-adjacent interior angles.
Let's first find the measure of angle P. We are given that m<P = 4/5(m<Q). Since these angles are interior angles of a triangle, their sum should be equal to 180 degrees. So we can set up the equation:
m<P + m<Q = 180
Substituting the given relationship, we get:
4/5(m<Q) + m<Q = 180
To solve for m<Q, we can multiply the entire equation by 5 to eliminate the fraction:
4(m<Q) + 5(m<Q) = 900
Simplifying the equation:
9(m<Q) = 900
Dividing both sides of the equation by 9, we find:
m<Q = 100
Therefore, the measure of angle Q in triangle PQR is 100 degrees.