Answer:
The measure of ∠PQW is 30°
Step-by-step explanation:
Given as :
The measure of angle WQR = ∠WQR = 130°
The measure of angle PQR = ∠PQR = 16x°
The measure of angle PQW = ∠PQW = 3x°
Now, From Figure
Since, The measure of angle ∠PQR = The sum of measure of angle ∠PQW + The sum of measure of angle ∠WQR
∴ ∠PQR = ∠PQW + ∠WQR
Or, 16x° = 3x° + 130°
Or, 16x° - 3x° = 130°
Or, 13x° = 130°
∴ x = [tex]\frac{130^{\circ}}{13^{\circ}}[/tex]
I.e x = 10°
Now, we put the value of x in angles
So, The measure of angle PQW = 3x°
I.e ∠PQW = 3 × 10°
∴ ∠PQW = 30°
The measure of ∠PQW = 30°
Hence The measure of ∠PQW is 30° Answer
