Math Problem Statement

Type the correct answer in each box. Use numerals instead of words. Consider ΔFGH.

A triangle F G H with two equal sides. Complete the following statements.

In ΔFGH, m∠F = 54°, m∠G = °, and m∠H = °.

Solution

In a triangle, the sum of the interior angles is always 180°. Since ΔFGH has two equal sides, it is an isosceles triangle, meaning that the two base angles are equal.

Given that m∠F = 54°, and the other two angles (m∠G and m∠H) are equal, we can solve for the remaining angles:

  1. Let m∠G = m∠H.
  2. The sum of the angles is 180°, so: 54°+2×mG=180°54° + 2 \times m∠G = 180° 2×mG=180°54°2 \times m∠G = 180° - 54° 2×mG=126°2 \times m∠G = 126° mG=63°m∠G = 63°

Thus, m∠G = 63° and m∠H = 63°.

Final Answer:

  • m∠G = 63°
  • m∠H = 63°

Would you like further details or have any questions?


Here are 5 related questions:

  1. How do you prove that the sum of angles in a triangle is always 180°?
  2. What are the properties of an isosceles triangle?
  3. Can a triangle have more than one obtuse angle?
  4. How do you calculate the angles in an equilateral triangle?
  5. What is the difference between an isosceles and a scalene triangle?

Tip: In an isosceles triangle, the angles opposite the equal sides are always equal.

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Math Problem Analysis

Mathematical Concepts

Geometry
Triangle Properties
Isosceles Triangle

Formulas

Sum of interior angles in a triangle: m∠F + m∠G + m∠H = 180°

Theorems

Sum of interior angles in a triangle
Properties of an isosceles triangle

Suitable Grade Level

Grades 6-8