The measure of ∠PQR will be 123° .
Interior Angles of an Angle:
An interior of an angle is a line that separates an angle into two angles. If BD is the interior of an angle ABC then the measure of the angle ABC is the sum of both the angles.
∠ABC = ∠ABD +∠DBC
We can divide an angle into many interior parts or angles.
If we have an angle and there are many interiors that divides the angle into many parts than the sum of all the interior angles is equal to the measure of the original angle.
If we have D and E are the two interiors of ∠ABC then ,
∠ABC =∠ABD + ∠DBE + ∠EBC
Given that point T is in the interior of ∠PQR and ∠PQR =10x-7
∠RQT = 5x°
∠PQT=(4x+6) .
Since T is the interior of ∠PQR ,
∠PQR = ∠PQT + ∠RQT
10x-7 = 4x + 6 + 5x
10x-7 = 9x + 6
x = 13°
So from the equation(1)-
∠PQR = 10(13) - 7
∠PQR = 123°
So ∠PQR = 123° .
To learn more on interior angles go here :
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