Question

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Answer 1

Answer:

1) ∠A=84°

2) ∠C=20°

Step-by-step explanation:

1)

First, find ∠C:

(I'm assuming the exterior angle of 126° makes a straight line with ∠C)

The angles on a straight line always add up to 180. Therefore:

∠C+126=180

∠C=180-126

∠C=54

Then find ∠B:

We also know that all the angles in a triangle add up to 180. Therefore:

∠A+∠B+∠C=180

∠A+∠B+54=180

∠A+∠B=126

(we know ∠A=2(∠B))

2(∠B)+∠B=126

3(∠B)=126

∠B=42

Now, find ∠A:

∠A=2(∠B)

∠A=2(42)

∠A=84°

2)

First, find ∠B:

(Again, I'm assuming the exterior angle of 100° makes a straight line with ∠B)

The angles on a straight line always add up to 180. Therefore:

∠B+100=180

∠B=180-100

∠B=80

Then find ∠A:

We also know that all the angles in a triangle add up to 180. Therefore:

∠A+∠B+∠C=180

∠A+80+∠C=180

∠A+∠C=100

(we know ∠A=4(∠C))

4(∠C)+∠C=100

5(∠C)=100

∠C=20°