Math Problem Statement

The measures of two angles of a triangle are given. Find the measure of the third angle. 63° 59', 108° 11' The measure of the third angle is (Simplify your answer. Type a whole number.)

Solution

To find the measure of the third angle in a triangle, we can use the fact that the sum of the angles in any triangle is always 180180^\circ.

Given angles:

  1. 635963^\circ 59'
  2. 10811108^\circ 11'

Let's first add these two angles together:

6359+10811=1727063^\circ 59' + 108^\circ 11' = 172^\circ 70'

Since 7070' is equivalent to 1101^\circ 10', the sum becomes:

17270=17310172^\circ 70' = 173^\circ 10'

Now, subtract this sum from 180180^\circ to find the third angle:

18017310=650180^\circ - 173^\circ 10' = 6^\circ 50'

Since the question asks for a whole number:

The measure of the third angle is 7.\text{The measure of the third angle is } 7^\circ.

Would you like more details or have any questions?


  1. How do you calculate the sum of angles in a triangle?
  2. What is the importance of angle sum property in triangles?
  3. Can a triangle have more than one obtuse angle?
  4. How would you handle non-standard angle measurements (like degrees and minutes)?
  5. Why do the angles in a triangle always add up to 180 degrees?

Tip: When dealing with angles in degrees and minutes, remember that 60 minutes (6060') make 1 degree (11^\circ).

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Math Problem Analysis

Mathematical Concepts

Geometry
Triangle properties

Formulas

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Theorems

Angle sum property of triangles

Suitable Grade Level

Grades 7-9