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Quadrilateral angles
Quadrilateral angles 256
Description
Exercise Name: Quadrilateral angles
Math Missions: 7th grade (U.S.) Math Mission, High school geometry Math Mission
Types of Problems: 1

The Quadrilateral angles exercise appears under the 7th grade (U.S.) Math Mission and High school geometry Math Mission. This exercise analyzes the relationships between angles in quadrilaterals.

Types of Problems

There is one type of problem in this exercise:

  1. Find the missing angle: This problem provides a diagram or describes a quadrilateral with some given information. Users are asked to find the measure of a particular angle and write it in the space provided.
    Qa1

    Find the missing angle

Strategies

Knowledge of the various quadrilaterals would help ensure completion of this exercise.

  1. The opposite angles in parallelograms are congruent, and adjacent angles are supplementary.
  2. In a trapezoid the adjacent angles between the bases are supplementary. In addition, if the trapezoid is isosceles, then there are two pairs of congruent angles.
  3. In a rectangle and square, all angles are right angles and measure {90^\circ}.
  4. In a kite one of the pairs of opposite angles are congruent, a quick sketch can tell which ones and this can be used to get some answers on this exercise.
  5. A rhombus is a parallelogram, and the kite rule also holds.

Real-life Applications

  1. Engineers and architects use angles for designs, roads, buildings and sporting facilities.
  2. Athletes use angles to enhance their performance.
  3. Carpenters use angles to make chairs, tables and sofas.
  4. Artists use their knowledge of angles to sketch portraits and paintings.
  5. The ancient Egyptians from over 4000 years ago were very good at shapes and geometry. Every time the Nile burst its banks and flooded the planes, they had to use geometry to measure their gardens and fields all over again.
  6. Architects use shapes to construct houses and skyscrapers.

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