If the measure of Arc U V is 84°, what is the measure of Angle Y U V? 42° 84° 96° 168°

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

°°

°° °

The measure of angle YUV is equal to m < YUV = 42°

the radius is 2 times the diameter.

step-by-step explanation: