The measure of angle YUV is equal to m < YUV = 42°
Step-by-step explanation:
Step 1:
we have that
arc UV = 84° -----> given problem
so
m < UZV = 84° ------> by central angle
Step 2:
we know that
The triangle UZV is an isosceles triangle
because
ZU = ZV = radius
so
m < ZUV = m < ZVU -----> bases angle of the isosceles triangle
Step 3:
Remember that
The sum of the internal angles of a triangle is equal to 180° so
m < ZUV + m < ZVU + m < UZV = 180°
2m < ZUV + m < UZV = 180°
Step 4:
substitute and solve for m<ZUV
2m < ZUV + 84° = 180°
m < ZUV = (180° - 84°) / 2 = 48°
m < ZUV + m < YUZ = 90° ------> by complementary angles
Step 5:
solve for m < YUZ
[tex]48[/tex]°[tex]+ m < YUV = 90[/tex]°
[tex]m < YUV = 90[/tex]°[tex]- 48[/tex]° [tex]= 42[/tex]°
The measure of angle YUV is equal to m < YUV = 42°
