in parallelogram lmno, what is the measure of angle n? 50° 70° 110° 130°
in parallelogram lmno, what is the measure of angle n? 50° 70° 110° 130°
Answer
Explanation:
Step1: Use property of parallelogram
In a parallelogram, adjacent - angles are supplementary. So, ((2x + 10)+(x + 20)=180).
Step2: Simplify the equation
Combine like - terms: (2x+x+10 + 20=180), which gives (3x+30 = 180).
Step3: Solve for x
Subtract 30 from both sides: (3x=180 - 30=150). Then divide both sides by 3: (x=\frac{150}{3}=50).
Step4: Find the measure of angle N
Angle N and angle O are adjacent. Angle O is (x + 20). Substitute (x = 50) into the expression for angle O: (O=50 + 20=70^{\circ}). Since adjacent angles in a parallelogram are supplementary, angle (N=180-(x + 20)). Substituting (x = 50), we get (N = 110^{\circ}).
Answer:
(110^{\circ})