Math Problem Statement

What is the measure of angle O in parallelogram LMNO?

Solution

To solve for the measure of angle OO in parallelogram LMNOLMNO, we will use properties of parallelograms and the given information from the image.

Step-by-step approach:

  1. Properties of a parallelogram: In any parallelogram, opposite angles are equal, and adjacent angles are supplementary (they add up to 180180^\circ).

  2. Given angles:

    • Angle LL is (x+40)(x + 40)^\circ.
    • Angle OO is (3x)(3x)^\circ.
  3. Relationship between angles LL and OO: Since LL and OO are adjacent angles in a parallelogram, they must add up to 180180^\circ. Therefore, we can write: (x+40)+(3x)=180(x + 40) + (3x) = 180

  4. Solve for xx: 4x+40=1804x + 40 = 180 Subtract 40 from both sides: 4x=1404x = 140 Divide by 4: x=35x = 35

  5. Find angle OO: Since Angle O=3x\text{Angle } O = 3x, substitute x=35x = 35: Angle O=3(35)=105\text{Angle } O = 3(35) = 105^\circ

Thus, the measure of angle OO is 105°.

Would you like more details or have any questions?


Here are 5 related questions to extend the problem:

  1. What is the measure of angle LL?
  2. How do you calculate angle MM in parallelogram LMNOLMNO?
  3. What would happen if the values of the angles were swapped?
  4. Can you verify if the opposite angles in parallelogram LMNOLMNO are equal?
  5. How would you check if the sides of parallelogram LMNOLMNO are congruent?

Tip: In any parallelogram, knowing one angle allows you to find all other angles due to symmetry and supplementary relationships!

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Math Problem Analysis

Mathematical Concepts

Geometry
Properties of Parallelograms
Algebra

Formulas

Sum of adjacent angles in a parallelogram: angle L + angle O = 180°
Expression for angle L: (x + 40)°
Expression for angle O: (3x)°

Theorems

Adjacent angles in a parallelogram are supplementary

Suitable Grade Level

Grades 8-10