Given that Angle OUR is congruent to Angle PUN and Angle OUR =2x+5,Angle RUN=4x-2 and Angle PUT= x+32,find the measure of Angle PUN
seems to me we need OUT angle
Again with the cryptic questions regarding an unseen diagram. How about this...
It appears that point U is at the center. Starting with point O, name the other points, in clockwise order around U.
If there are polygons formed by some of the points, name their vertices in clockwise order.
To find the measure of angle PUN, we can use the information given and solve for x. Then, we can substitute the value of x into the expression for angle PUN to find its measure.
According to the information provided, we know that angle OUR is congruent to angle PUN.
So, angle OUR = angle PUN.
Given that angle OUR = 2x + 5, we can substitute angle PUN with 2x + 5, and we have:
2x + 5 = angle PUN.
Now, we need to find the value of x.
We also know that angle RUN = 4x - 2.
Given that angle RUN = angle PUT, we can set up the equation:
4x - 2 = x + 32.
Now, let's solve for x:
4x - x = 32 + 2,
3x = 34,
x = 34/3.
Now that we know the value of x, we can substitute it into the expression for angle PUN:
Angle PUN = 2x + 5
= 2(34/3) + 5
= 68/3 + 5
= 68/3 + 15/3
= 83/3.
Therefore, the measure of angle PUN is 83/3 units.