The m∠POS would be - 65° by the angle addition postulate and substitution postulate.
Given, m∠POQ = 19° , m∠QOR = 31° and m∠ROS = 15°
Angle Addition Postulate is the measure of the larger angle is the sum of the measures of the two smaller angles.
Substitution postulate states that a quantity may be substituted for its equality in any expression.
Then substitute the angle measurements into the resulting equation to find, m∠POS:
m∠POQ + m∠QOR = m∠POR (by angle addition)
m∠POR + m∠ROS = m∠POS (by substitution)
m∠POS = m∠POQ + m∠QOR + m∠ROS
= 19° + 31° + 15°
= 65°
Thus, the m∠POS would be - 65° by the angle addition postulate and substitution postulate.
Learn more about Angle addition postulate here:
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