Find the angles marked in letters.

Answers:

Explanations:

Problem 1

The interior angles of any quadrilateral always add to 360.

So we solve 82+84+A+78 = 360 for A and we'll have these steps

82+84+A+78 = 360

A+244 = 360

A = 360-244

A = 116

Problem 2

Same idea as the previous problem. This time we need to solve the equation 110+130+B+53 = 360

So,

110+130+B+53 = 360

B+293 = 360

B = 360-293

B = 67

Problem 3

Same idea as the other previous problems.

The equation to solve is 40+A+71+80 = 360

I'll skip the steps for it unless you need me to show them.

You should get a final answer of A = 169

Problem 4

Focus on the triangle with interior angles of: A, 68, 62

For any triangle, the three angles always add to 180

A+68+62 = 180

A+130 = 180

A = 180-130

A = 50
Now focus on the quadrilateral with interior angles of: B, 68, 62, 88

Like with problems 1 through 3, the quadrilateral angles add to 360

The equation to solve is B+68+62+88 = 360 and you should isolate B to get B = 142

Lastly, focus on the triangle with interior angles of: 88, C, 62

The equation to solve is 88+C+62 = 180. You should get C = 30

Let me know if you need to see the steps. They are similar to the other set of steps shown earlier.

Problem 5

Focus on the triangle with interior angles of: A, 62, 35

We have these steps that will find angle A

A+62+35 = 180

A+97 = 180

A = 180-97

A = 83

Move your attention to the quadrilateral with interior angles of: C, 62, 35, 119

Those four angles add to 360

C+62+35+119 = 360

C+216 = 360

C = 360-216

C = 144

Notice how this angle C is adjacent and supplementary to angle B

I.e. the linear pair of angles add to 180

B+C = 180

B+144 = 180

B = 180-144

B = 36

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step-by-step explanation:

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step-by-step explanation: