Question

in the diagram of circle A, what is the measure of XYZ?
A.35
B.70
C.75
D.140

Answer 1

Answer:

C. 75

Step-by-step explanation:

Answer 2

A straight line that intersects a circle in two points is called a secant line. A chord is the line segment that joins two distinct points of the circle. A chord is in a unique secant line and every secant line defines a unique chord.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is constant.

In geometry, the tangent line to a plane curve at a given point is the straight line that "just touches" the curve at that point. Leibniz defined it as the line through a pair of infinitely close points on the curve.

Given,

Measure of arc $WZ = 175^\circ$

Measure of angle $XAZ = 105^\circ$

We have to find the measure of angle XYZ.

We know, the angle subtended at the center is the average of the measure of arc intercepted by its angle and its vertical angles.

So, $\frac{175^\circ+\angle XYZ}{2}=105^\circ$

$175^\circ + \angle XYZ = 210^\circ$

$\angle XYZ = 210^\circ - 175^\circ$

$\angle XYZ = 35^\circ$

Therefore, the value of $\angle XYZ = 35^\circ$

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