In the figure below, m∠R is 64°, and m∠T is 123°.
Note: Figure is not drawn to scale.
What is m∠Q?
A.
57°
B.
26°
C.
59°
D.
121°
To find the measure of angle Q, we need to apply the Angle Sum Theorem.
The Angle Sum Theorem states that the sum of the measures of the interior angles of any triangle is 180°.
Therefore, we can set up an equation:
m∠R + m∠T + m∠Q = 180°
Substituting in the given values:
64° + 123° + m∠Q = 180°
Simplifying the equation:
187° + m∠Q = 180°
Subtracting 187° from both sides:
m∠Q = 180° - 187°
m∠Q = -7°
Since angles cannot have negative measures, this does not make sense.
Therefore, there must be an error in the given information or in the equation set up.