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:
- Let m∠G = m∠H.
- The sum of the angles is 180°, so:
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:
- How do you prove that the sum of angles in a triangle is always 180°?
- What are the properties of an isosceles triangle?
- Can a triangle have more than one obtuse angle?
- How do you calculate the angles in an equilateral triangle?
- 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