Textbook Question
In each figure, there are two similar triangles. Find the unknown measurement. Give any approximation to the nearest tenth.
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1. Measuring Angles
Complementary and Supplementary Angles
2:01 minutesProblem 28
Textbook Question
The measures of two angles of a triangle are given. Find the measure of the third angle. See Example 2.
29.6° , 49.7°
Verified step by step guidance1
Recall that the sum of the interior angles of any triangle is always 180 degrees. This is a fundamental property of triangles.
Identify the given angles: the first angle is 29.6° and the second angle is 49.7°.
Set up an equation to find the third angle, which we can call \( x \):
\[ 29.6 + 49.7 + x = 180 \]
Combine the known angles on the left side:
\[ 79.3 + x = 180 \]
Solve for \( x \) by subtracting 79.3 from both sides:
\[ x = 180 - 79.3 \]
Verified video answer for a similar problem:This video solution was recommended by our tutors as helpful for the problem above
Video duration:
2mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Triangle Angle Sum Property
The sum of the interior angles of any triangle is always 180 degrees. This fundamental property allows us to find the measure of an unknown angle when the other two angles are known by subtracting their sum from 180°.
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Basic Arithmetic Operations
Solving for the unknown angle requires simple arithmetic, specifically addition and subtraction. Adding the two given angles and subtracting their sum from 180° yields the measure of the third angle.
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Angle Measurement Units
Angles are measured in degrees (°), a unit that divides a full rotation into 360 parts. Understanding this unit is essential for interpreting the given angle measures and performing calculations accurately.
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