Question

Find m∠PQW if m∠WQR = 130°, m∠PQR = 16x, and m∠PQW = 3x.

A) 5°
B) 10°
C) 30°
D) 40°

Pls answer i need this fast

Answer 1

The measure of ∠PQW is 30°

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 =
`(130^(\circ))/(13^(\circ))`

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