Question
Question 9 of 9 \( \triangle A B C \) contains two angles that measure 72 and 23 degrees each. \( \triangle D E F \) also contains two angles that measure 72 and 23 degrees. The measure of the third angles of both triangles must be degrees.
Ask by Ortiz Page. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
Both third angles measure 85 degrees.
Solution
To determine the measure of the third angle in both triangles \( \triangle ABC \) and \( \triangle DEF \), we can use the fact that the sum of the interior angles in any triangle is always 180 degrees.
Given:
- Two angles in each triangle are 72 degrees and 23 degrees.
Calculate the third angle:
\[
\text{Third angle} = 180^\circ - (72^\circ + 23^\circ) = 180^\circ - 95^\circ = 85^\circ
\]
**Answer:**
Both third angles measure 85 degrees.
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Simplify this solution Beyond the Answer
In any triangle, the sum of all three angles is always 180 degrees. So for \( \triangle ABC \), you just add the two known angles (72 degrees and 23 degrees) and subtract from 180: \( 180 - (72 + 23) = 85 \) degrees. Thus, the third angle in \( \triangle ABC \) is 85 degrees. Similarly, for \( \triangle DEF \), since it has the same angles as \( \triangle ABC \), the calculation is identical. You will also find that the third angle measures 85 degrees. It's fascinating how geometric properties remain consistent across similar shapes!
