Math Problem Statement

Find the unknown angles in the following triangle

Solution

To find the unknown angles in the given triangles, I'll analyze each triangle step-by-step. Here are the detailed explanations for each triangle:

Triangle (a)

  • Given: One angle is 7676^\circ.
  • Solution: Since the sum of the angles in a triangle is always 180180^\circ, the unknown angle xx can be found as: x=1807690=14.x = 180^\circ - 76^\circ - 90^\circ = 14^\circ.

Triangle (b)

  • Given: Right triangle with angles 3030^\circ and xx.
  • Solution: Using the triangle angle sum property: x=1809030=60.x = 180^\circ - 90^\circ - 30^\circ = 60^\circ.

Triangle (c)

  • Given: Right triangle with sides labeled, angles of 9090^\circ, 5252^\circ, and xx.
  • Solution: We know: x=1805290=38.x = 180^\circ - 52^\circ - 90^\circ = 38^\circ.

Triangle (d)

  • Given: One angle is xx, a triangle marked as right-angled.
  • Solution: We use 1807290=18.180^\circ - 72^\circ - 90^\circ = 18^\circ.

Triangle (e)

  • Given: An obtuse triangle with 108108^\circ and side lengths labeled.
  • Solution: To find xx: x=180108remainingside72.x = 180^\circ - 108^\circ - remaining side 72.

Do confirm such results accuracy expectations further working if needing verify cross-check back deeper aspects approaches.

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Math Problem Analysis

Mathematical Concepts

Triangle Properties
Angle Sum Property
Right Triangle Properties

Formulas

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Theorems

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Suitable Grade Level

Grades 7-9