Given: Circle k(O), diameter US , m RU=50°, m UT=30° Find: m∠RUS, m∠STU

From the diagram of circle k(O), m∠RUS = 65° and m∠STU = 90°

Given that:

m∠ORU = m∠OUR (isosceles triangle)

m∠ORU + m∠OUR + m∠ROU = 180° (angle in triangle)

50 + 2 * m∠OUR = 180

m∠OUR = 65°

m∠OUR =  m∠RUS = 65°

m∠STU = 90° (angle subtended at circumference by semicircle).

From the diagram of circle k(O), m∠RUS = 65° and m∠STU = 90°

Find out more on circle theorems at: link

Step-by-step explanation:

Given that RU = 50°, So Central Angle ROU = 50° too because the measure of arc is equal to its central angle

Now, Let's assume a triangle ROU. It is an isosceles triangle since RO = RU (Radii of the same circle)

So,

∠ORU ≅ ∠OUR (Angles opposite to equal sides are equal)

So, we can write them as 2(∠RUO)

So,

2(∠RUO)+50 = 180 (Interior angles of a triangle add up to 180)

2(∠RUO) = 180-50

2(∠RUO) = 130

Dividing both sides by 2

∠RUO = 130/2

∠RUO = 65 degrees

m∠RUS = 65 degrees  (Both are the same)

In a semi circle (Given that SU is a diameter) , there must be a 90 degrees angle sin it opposite to the diameter.

So,

m∠STU = 90 degrees

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3