Math Problem Statement

Solve problems, 16, 18 and 20

Solve problems 16, 18, and 20.

Solution

Let's address the requested problems from the image.

Problem 16:

Draw a figure that fits each description - an acute angle, ∠GHJ.

  • An acute angle is an angle that measures less than 90 degrees. For ∠GHJ, you would draw two rays that meet at point H, ensuring that the angle between them is less than 90°. This could be any measurement from 0° to less than 90°.

Problem 18:

Use the diagram below. Complete each statement - ∠CBJ ≅ ∠___.

  • The notation "≅" stands for "congruent to," meaning the angles have the same measurement.
  • Without the diagram, it's not possible to identify the specific angle congruent to ∠CBJ. However, based on typical geometric problems, you would look for an angle with the same measurement, either through symmetry or other geometric properties (like corresponding or alternate angles).

Problem 20:

If m∠EFD = 75°, then m∠JAB = ___.

  • Given that m∠EFD = 75°, we are asked to find the measurement of ∠JAB. Since we don’t have the diagram for reference, it's likely this problem uses a supplementary, complementary, or some geometric rule (parallel lines, etc.).
    • If ∠EFD and ∠JAB are corresponding angles, or if some geometric property links them, then ∠JAB = 75°.
    • If the two angles are supplementary (add up to 180°), then m∠JAB = 180° - 75° = 105°.

Please refer to the diagram to determine the exact relationship between the angles.


Would you like more details or have further questions on any of these problems?

Here are 5 related questions for further practice:

  1. What are the properties of congruent angles?
  2. How do you find the measure of supplementary angles?
  3. Can an obtuse angle be congruent to an acute angle?
  4. How would you classify an angle measuring exactly 90°?
  5. What geometric rules can help find angle congruences in a diagram?

Tip: When solving geometry problems, always analyze the relationships between angles using properties like congruence, supplementarity, or angle sum in polygons.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Angles
Congruent Angles
Acute Angles
Supplementary Angles

Formulas

m∠1 + m∠2 = 180° (supplementary angles)

Theorems

Congruent Angles Theorem
Supplementary Angles Theorem

Suitable Grade Level

Grades 6-8