QS−→ bisects ∠PQR. If ∡PQS=3x and ∡RQS=2x+6,then what is ∡PQR ?
but you just said that
3 x = 2 x + 6
so
x = 6
then 3 x = 18 = 2x+6
and then 2 * 18 = 36
DRAW IT !!!
bisecting divides PQR into two EQUAL angles
∡PQS = ∡RQS ... 3x = 2x + 6 ... x = 6
∡PQR = ∡PQS + ∡RQS
To solve this problem, we will use the fact that a bisector divides an angle into two congruent angles.
Given:
∠PQS = 3x
∠RQS = 2x + 6
Since QS bisects ∠PQR, we can assume that the two angles formed are congruent.
Let's label one of the congruent angles as ∠PQS = ∠SQR = 3x.
Then, we can set up an equation based on the angles in a triangle:
∠PQR + ∠PQS + ∠RQS = 180°
Substituting the given values:
∠PQR + 3x + (2x + 6) = 180°
Combining like terms:
∠PQR + 3x + 2x + 6 = 180°
∠PQR + 5x + 6 = 180°
Subtracting 6 from both sides:
∠PQR + 5x = 174°
Subtracting 5x from both sides:
∠PQR = 174° - 5x
Therefore, ∠PQR is 174° - 5x.