One of the angles of an isosceles triangle measures 96^∘ . What is the measure of the largest an

Name: Problem 22, Chapter 3: Elementary Geometry for College Students
Uploaded: 2021-07-10T06:47:01-08:00
Duration: 1 min 59 s
Channel: Pronoy Sinha
Description: One of the angles of an isosceles triangle measures 96^∘ . What is the measure of the largest angle(s) of the triangle? What is the measure of the smallest angle(s) of the triangle?

step 1 This is an isosceles triangle which has two equal sides. If an angle of an isisorice triangle me

Question

One of the angles of an isosceles triangle measures $96^{\circ} .$ What is the measure of the largest angle(s) of the triangle? What is the measure of the smallest angle(s) of the triangle?

   One of the angles of an isosceles triangle measures $96^{\circ} .$ What is the measure of the largest angle(s) of the triangle? What is the measure of the smallest angle(s) of the triangle?

Elementary Geometry for College Students

Daniel C. Alexander,… 6th Edition

Chapter 3, Problem 22

Instant Answer

Solved by Expert Pronoy Sinha

07/10/2021

Step 1

Given that one of the angles in the isosceles triangle is $96^{\circ}$, we can represent the other two equal angles as $x$. Show more…

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One of the angles of an isosceles triangle measures $96^{\circ} .$ What is the measure of the largest angle(s) of the triangle? What is the measure of the smallest angle(s) of the triangle?

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Key Concepts

Isosceles Triangle

An isosceles triangle is a triangle with at least two sides that are equal in length, which directly implies that the angles opposite those equal sides are also equal. This property is crucial for determining unknown angles when one angle measure is given, as it establishes a symmetry that simplifies the calculations.

Triangle Angle Sum Theorem

The Triangle Angle Sum Theorem states that the sum of the interior angles of any triangle is always 180°. This fundamental principle is essential for solving many triangle-related problems, including finding unknown angles when one or two angle measures are given.

Base Angles Theorem

In an isosceles triangle, the angles opposite the equal sides are equal. This theorem allows us to deduce that if the known angle is not repeated, then the other two angles must be equal and can be found by subtracting the given angle from 180° and dividing the result by two.

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