Q14) Points A, B and C lie on the circumference of a circle and DE is the
tangent to the circle at A. Angle DAB = 79º and angle EAC = 37º.
2
Find the sizes of angles x and y.
Not to scale
Give a reason for your answers.
B
7
[Total 3
790
1370
E
A

x = 37

y = 79

Step-by-step explanation:

Remark

We are going to go through an extensive discussion of the value of x. The value for y is found exactly the same way.

Top diagram.

The top diagram establishes the fact that if any two points are on the major arc of the circle whose center is 0, then the vertex of the of the two angles so formed are equal. The end points of these two angles must be established by the endpoints of the chord A and B.

Put in much simpler language.

<ACB = <AC'B

The end points of the angles are A and B of the Chord AB.

The Vertex of the angles are both on the major arc of the circle. These two are C and C'

Bottom Diagram

The idea here is to find the value of C. If we do that, then we know what x is in the diagram you provided.

Draw diameter COA       Construction

< CAB = 90                      Any vertex (C) on circumference with diameter endpoints (A & C) = 90

<CAT_1 = 90                   A diameter always meets a tangent at 90o

<BAT_1 = 37                   Given

<CAB = 90-37                  <CAB and <BAT_1 are complementary

<ACB = 37                       A right triangle's acute angles are complementary.

<ACB = x = 37o              See top diagram

the central idea is that:

individuals should refuse to cooperate with institutions they believe unjust.

thoreau felt  that governments were more often agents of corruption than justice, even democracies, and that just because the majority feels a certain way does not make it just or correct in absolute terms. he uses the fact that slavery exists in our democracy to support this idea.

he goes on to say that, as a result, people should live true to their own internal laws regarding right and wrong, as a product of reflection and a moral life, rather than following every law that society imposes. 

step-by-step explanation:

none cuz there are no "following statements" regarding the question

step-by-step explanation: