Math Problem Statement

Find the missing angles of the triangles given two angles in each problem.

Solution

It looks like the worksheet you uploaded is focused on finding missing angles in triangles based on the interior angle sum property. This property states that the sum of the interior angles of any triangle is always 180°. I will guide you through the solution of each problem on the sheet.

Let me summarize the problems and their solutions:

  1. First triangle:

    • Given angles: 9090^\circ and 26.326.3^\circ
    • The sum of angles in a triangle is 180180^\circ, so the missing angle α\alpha can be found by: α=1809026.3=63.7\alpha = 180^\circ - 90^\circ - 26.3^\circ = 63.7^\circ
    • α=63.7\alpha = 63.7^\circ
  2. Second triangle:

    • Given angles: 61.861.8^\circ and 75.275.2^\circ
    • The missing angle kk is: k=18061.875.2=43k = 180^\circ - 61.8^\circ - 75.2^\circ = 43^\circ
    • k=43k = 43^\circ
  3. Third triangle:

    • Given angles: 80.580.5^\circ and 80.580.5^\circ (Isosceles triangle)
    • The missing angle vv is: v=18080.580.5=19v = 180^\circ - 80.5^\circ - 80.5^\circ = 19^\circ
    • v=19v = 19^\circ
  4. Fourth triangle:

    • Given angles: 5858^\circ and 33.733.7^\circ
    • The missing angle ee is: e=1805833.7=88.3e = 180^\circ - 58^\circ - 33.7^\circ = 88.3^\circ
    • e=88.3e = 88.3^\circ
  5. Fifth triangle:

    • Given angles: 42.442.4^\circ and 1414^\circ
    • The missing angle yy is: y=18042.414=123.6y = 180^\circ - 42.4^\circ - 14^\circ = 123.6^\circ
    • y=123.6y = 123.6^\circ
  6. Sixth triangle:

    • Given angles: 32.632.6^\circ and 61.761.7^\circ
    • The missing angle ff is: f=18032.661.7=85.7f = 180^\circ - 32.6^\circ - 61.7^\circ = 85.7^\circ
    • f=85.7f = 85.7^\circ

Would you like any more details or clarifications?

Here are 5 related questions you can try:

  1. What is the sum of the angles in a quadrilateral?
  2. If one angle of a right triangle is 5050^\circ, what is the other angle?
  3. How can we find the exterior angle of a triangle?
  4. What is the sum of the interior angles of a pentagon?
  5. Can a triangle have more than one obtuse angle?

Tip: Always verify the type of triangle (e.g., right, isosceles, equilateral) to ensure your angle calculations make sense based on its properties.

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Math Problem Analysis

Mathematical Concepts

Geometry
Triangle Angle Sum

Formulas

Sum of interior angles of a triangle: 180°

Theorems

Triangle Angle Sum Theorem

Suitable Grade Level

Grades 6-8