QR (with an arrow line above it) is the interior of angle PQS, then m angle PQR + m angle RQS = m angle PQS
well, since
anglePQR + angleRQs = anglePQS
multiply each term by m would give you your result, wouldn't it?
true. This is just angle addition.
The measure of the outside angle is the sum of the measures of the two adjacent angles.
So, why can't we just add angles, instead of all this "measure" stuff?
To prove the statement that m angle PQR + m angle RQS = m angle PQS when QR (with an arrow line above it) is the interior angle, we need to use the properties of angles and the concept of interior angles.
1. Start with angle PQS: This is the entire angle formed by lines PQ and QS.
2. Split angle PQS into two smaller angles: Draw a line QR within angle PQS (with the arrow line above it) to create angle PQR and angle RQS.
3. Understand interior angles: Interior angles are formed when two lines intersect inside a shape or region. In this case, angle PQR and angle RQS are interior angles of angle PQS.
4. Prove the statement: To prove that m angle PQR + m angle RQS = m angle PQS, we need to show that the sum of the measures of angle PQR and angle RQS is equal to the measure of angle PQS.
Let's consider the Proof:
Start with angle PQS (the entire angle).
Split it into angle PQR and angle RQS by drawing line QR through its interior.
Now, we will use the Angle Addition Postulate, which states that the measure of the whole angle is equal to the sum of the measures of its parts.
According to this postulate, we can write:
m angle PQS = m angle PQR + m angle RQS
This equation tells us that the sum of the measures of the smaller angles, angle PQR and angle RQS, is equal to the measure of the larger angle, angle PQS.
Thus, the statement m angle PQR + m angle RQS = m angle PQS holds true when QR (with an arrow line above it) is the interior of angle PQS.