Question
Download Solution PDFThe measures of the three angles of a triangle are such that the smallest angle measures 42º less than the greatest angle, while the measure of the remaining angle is 24º more than the measure of the smallest angle. Find the measure of the smallest angle of the triangle.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The smallest angle measures 42º less than the greatest angle.
The remaining angle is 24º more than the smallest angle.
Formula Used:
Sum of angles in a triangle = 180º
Calculation:
Let the smallest angle be x º.
Largest angle = x + 42 º
Remaining angle = x + 24°
Sum of angles: x + (x + 42) + (x + 24) = 180 º
⇒ 3x + 66 = 180
⇒ 3x = 180 - 66
⇒ 3x = 114
⇒ x = 38
Smallest angle = x = 38°.
The measure of the smallest angle of the triangle is 38º.
Last updated on May 28, 2025
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