Question

Angles: Arcs & Angles need help thank you!!

Answer 1

Answer:

See answers below

Step-by-step explanation:

1) The typr of triangle in a semicircle is a right angle. Hence the measure of  m<ABC  is 90degrees

2) m<DEF = 1/2(144)

m<DEF = 144/2

m<DEF = 72degrees

3) From the trinagle

4x+3 + x+7 +90 ==180

5x + 100 = 180

5x = 180-100

5x = 80

x = 80/5

x = 16

<QRD =  x+7

m<QRD = 16 + 7

m<QRD = 23degrees

4)  Angle in the same segment are equal

5x-37= 3x+1

5x - 3x = 1+37

2x = 38

x = 38/2

x =19

arc NM = 2m<P

arc NM = 2(3x+1)

arc NM = 2(3(19)+1)

arc NM = 2(58)

arcNM = 116degrees