Q1. 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
Q2. Given that Angle TUN and Angle PUN are complementary angles and Abgle OUR = 4<RUP,what is the measure of Angle OUR.
To solve the problems, we need to use the properties of congruent angles, complementary angles, and the relationships between angle measurements in a triangle. Let's break down each problem step by step.
Q1:
1) We are given that Angle OUR is congruent to Angle PUN. This means that Angle OUR = Angle PUN.
2) We are also given that Angle OUR = 2x + 5.
3) To find the measure of Angle PUN, we substitute Angle OUR with its given value: Angle PUN = 2x + 5.
Q2:
1) We are given that Angle TUN and Angle PUN are complementary angles. Complementary angles add up to 90 degrees. Therefore, Angle TUN + Angle PUN = 90.
2) We are also given that Angle OUR = 4 * Angle RUP.
3) To find the measure of Angle OUR, we need to determine the value of Angle RUP.
4) We know that the sum of the angles in a triangle is 180 degrees. So, Angle RUP + Angle RUN + Angle URN = 180.
5) Angle RUN = 4x - 2 and Angle URN = Angle PUT = x + 32.
6) Substituting the given values, we have (4x - 2) + (x + 32) + (x + 32) = 180.
7) Solve the equation to find the value of x.
8) Once x is determined, substitute it into Angle RUP = 4x - 2.
9) Finally, substitute the value of Angle RUP into Angle OUR = 4 * Angle RUP to find the measure of Angle OUR.
By following these steps and applying the properties of angles in a triangle, you can find the measures of Angle PUN and Angle OUR.