Question

Use the diagram to find the measure of each of the angles.

AQB
180 > x > 90
x = 90
x > 180
x < 90

ASB
180 > x > 90
x = 90
x > 180
x < 90

ALB
180 > x > 90
x = 90
x > 180
x < 90

ATB
180 > x > 90
x = 90
x > 180
x < 90

ARB
180 > x > 90
x = 90
x > 180
x < 90

BWD
180 > x > 90
x = 90
x > 180
x < 90

Answer 1

Angle AQB is x = 90

Angle ASB is x = 90

Angle ALB is x = 90

Angle ATB is x = 90

Angle ARB is x = 90

BWD is x < 90

Answer 2

If an angle is inscribed in a semicircle, it will be half the measure of a semicircle (180°), that is, measuring 90 degrees.

According to the given diagram,

Q, S, L, T, R and W are the points of the circumference of the circle having center O,

Also, AB is the diameter of the given circle,

∠AQB, ∠ASB, ∠ALB, ∠ATB, ∠ARB and ∠AWB are the angles on the semicircle,

Thus, by the above property,

m∠AQB = 90°

m∠ASB = 90°

m∠ALB = 90°

m∠ATB = 90°

m∠ARB = 90°

m∠AWB = 90°

If m∠BWD = x

Since, By the diagram,

m∠BWD < m∠AWD

⇒ m∠BWD < 90°

⇒ x < 90°