, 15.05.202020201947

# Find the value of ? in the given illustration. Show complete solution. #math #Triangle Inequality  maledabacuetes cleik

1. {2,4,5,6}

2. {1,6}

3. {6}

4. same answer in number 1

5. same answer in number 2

6. same answer in number 3 reyquicoy4321

a.) 70°

b.) angle TUY = 120°

Step-by-step explanation:

Triangle Angle Sum Theorem

It states that the three interior angles of a triangle is equal to 180°.

Supplementary Angles

Supplementary angles are two angles, that are commonly lies on the same side of a straight line, with a sum of 180 degrees.

Solution:a.)

Given:

T = 50°

RVU = 120°

U = ?

T + U + V = 180°

Notice that angle TVU and angle RVU are supplementary angles.

Hence, TVU + RVU = 180°

TVU + 120° = 180°

TVU = 180° - 120°

TVU = 60°

since, TVU = V

Therefore, V = 60°

From the eq. T + U + V = 180°

50° + U + 60° = 180°

U = 180° - 50° - 60°

U = 180° - 110°

U = 70°

b.)

Given:

S = 70°

T = 50°

TUY = ?

S + T + U = 180°

70° + 50° + U = 180°

U = 180° - 70° - 50°

U = 180° - 120°

U = 60°

Notice that angle SUT and angle TUY are supplementary angles.

Hence, SUT + TUY = 180°

Since SUT = U ,

Therefore,

U + TUY = 180°

60° + TUY = 180°

TUY = 180° - 60°

TUY = 120°

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