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Answer:

See below

Step-by-step explanation:

The picture is dark and I presume the given exterior angle of the larger triangle is 138°

Anyway, whatever it is, you say you have solved for m∠1

The smaller rectangle has a side extended so that ∠1 becomes an exterior angle

By the exterior angle postulate,

measure of exterior angle = sum of measures of opposite interior angles
m∠1 = m∠2 + 85°

and
m ∠2 = m ∠1 - 85°

1751659

Answer:

View below.

Step-by-step explanation:

So, unluckily, ∡2 isn't on a straight line so it would require more steps, however, we can simply solve them.

Sum of angles in a Δ and straight line:

We know that the sum of angles on a line is 180˚. We also know that a sum of angles in a triangle is 180˚ so now we have to use these formulae!

Finding ∡1:

To find ∡1, we will first have to find the length of [tex]x[/tex], located below ∡1.

  • [tex]x=180-138[/tex]
  • [tex]x=42[/tex] ˚

Now that we know the value of [tex]x[/tex], we need to find the value of 1. By doing so, we need to use the sum of angles in a Δ.

  • [tex]1_{angle} =180-42-18[/tex]
  • [tex]1_{angle} =138-18[/tex]
  • [tex]1_{angle} =120[/tex] ˚

Now that we found the value of 1, we know that it is 120˚

Finding ∡2:

To find ∡1, we will first have to find the length of [tex]y[/tex], located above ∡1.

  • [tex]y=180-120[/tex]
  • [tex]y=60[/tex] ˚

We need to find the value of 2. By doing so, we need to use the sum of angles in a Δ.

  • [tex]2_{angle} =180-60-85[/tex]
  • [tex]2_{angle} =120-85[/tex]
  • [tex]2_{angle} =35[/tex]˚

∴ we know ∡1 and ∡2 is 120˚ and 35˚ respectively.

Cheers! Hope this helps!

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