Math Problem Statement

Find the measure of the missing angles: d, e, and f, with a given angle of 72 degrees.

Solution

In this diagram, we are given a few angles and asked to find the missing ones: dd, ee, and ff. Let's analyze the relationships:

  1. Angle dd: The angle marked dd is a right angle, shown by the symbol indicating 90°. Therefore, d=90d = 90^\circ.

  2. Angle ee: Angle ee forms a linear pair with the angle marked 7272^\circ. Linear pairs are supplementary, meaning their sum is 180180^\circ. Hence, we can calculate ee as: e=18072=108e = 180^\circ - 72^\circ = 108^\circ

  3. Angle ff: Angle ff is vertically opposite to the given 7272^\circ angle. Vertically opposite angles are equal, so: f=72f = 72^\circ

Final Answers:

  • d=90d = 90^\circ
  • e=108e = 108^\circ
  • f=72f = 72^\circ

Would you like more details or have any further questions?


Here are 5 related questions to think about:

  1. What are vertically opposite angles, and why are they equal?
  2. How do you calculate the measure of an angle in a linear pair?
  3. What are complementary and supplementary angles?
  4. Can a triangle have a 90° angle and still have two equal angles? Why or why not?
  5. How can the concept of angle bisectors help in solving angle problems?

Tip: Remember, linear pairs always sum to 180°, and vertically opposite angles are always equal!

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Math Problem Analysis

Mathematical Concepts

Angles
Linear Pair
Vertically Opposite Angles

Formulas

Sum of angles in a linear pair: 180°
Vertically opposite angles are equal

Theorems

Linear Pair Theorem: The sum of angles on a straight line is 180°.
Vertically Opposite Angle Theorem: Opposite angles formed by two intersecting lines are equal.

Suitable Grade Level

Grades 6-8