Question

In cyclic quadrilateral WXYZ, the measure of angle Z is 10 more than twice the average of the measures of other three angles. The measure of angle Z, is:
1. 150
2. 30
3. 120
4. 60

Answer 1

Correct Answer - Option 1 : 150

Given :

Cyclic quadrilateral  = WXYZ

The measure of angle Z is 10 more than twice the average of the measures of other three angles

The measure of angle Z = ?

Calculation :

A quadrilateral will have 4 angles totaling 360 degrees.

w + x + y + z =360

We also know that z is 10 more than twice the average of the other 3 angles. 

z = 2 × (w + x + y)/3 +10

w + x + y + 2 × (w + x + y)/3 +10 =360

5/3 × (w + x + y) + 10 = 360 

5/3 × (w + x + y) = 350 

w + x + y = 210

z = 360 - 210 = 150 

∴ The measure of angle z is 150