Two angles are supplementary. One of them is an acute angle. Which of
these could be the measure of the other angle? *
Mark only one oval.
60° 90° 120° 180°
Answers
Answer:
120 can be the measure of other angle
Given: two angles are supplementary one of them acute angle
To Find: Which of these could be the measure of the other angle?
60° 90° 120° 180°
Solution:
Two angles are said to be supplementary if their measures adds up to 180°.
Acute angles measure between 0° and 90°
Obtuse angle measure between 90° and 180°
Right angle measures 90°
0° < Acute angle < 90°
90° < obtuse angle < 180°
Right angle = 90°
one angle is acute
Let say other angle = x
x + Acute angle = 180°
=> x = 180° - Acute angle
0° < Acute angle < 90°
Multiplying by -ve
=> 0° > -Acute angle > -90°
Adding 180° each side
=> 180° > 180° - Acute angle > 90°
=> 180° > x > 90°
Hence x is obtuse angle
x lies between 90° and 180°
In the given options only 120° satisfies that
Hence measure of the other angle can be 120°
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