Question

What are the measures of 1 and 2? 37.1 1 2 17.30 121.8°​

Answer 1

Answer:

Option 2 : m∠1 = 67.4°, m∠2 = 104.5°

Step-by-step explanation:

Lets find the measure of angle 2 first:

180° - 17.3° - (180° - 121.8°) = Angle 2

                             ↑

             Angle of the straight line = 180°

             The angle should be 180 - 121.8

Angle 2 = 104.5

At this point the only answer that works is the second option, but let's still work out Angle 1

Angle 1 :

Theory of opposite angles state that the opposite angles inside a triangle = the exterior angle

in this case:

Angle 1 + 37.1 = Angle 2

Since we know angle 2 = 104.5, lets solve

Lets say angle 1 = x

x + 37.1 = 104.5

x = 104.5 - 37.1

x = 67.4

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Answer 2

To find:-

The measures of ∠ 1 and ∠ 2.

Solution:-

${\boxed{\mathcal{\red{Angle\: 1 \:=\: 67.4° \:}}}}$✅

${\boxed{\mathcal{\red{Angle\: 2\:=\:104.5° \:}}}}$✅

Step-by-step explanation:-

We know that,

$\sf\purple{Sum\:of\:angles\:on\:a\:straight\:line\:=\:180°}$

✒ ∠ x + 121.8° = 180°

✒ ∠ x = 180° - 121.8°

✒ ∠ x = 58.2°

Now,

$\sf\pink{Sum\:of\:angles\:of\:a\:triangle\:=\:180°}$

➪ ∠ 2 + 17.3° + 58.2° = 180°

➪ ∠ 2 + 75.5° = 180°

➪ ∠ 2 = 180° - 75.5°

➪ ∠ 2 = 104.5°

$\boxed{Therefore,\:the\:measure\:of\:∠\:2\:is\:104.5°.}$

Again,

$\sf\blue{Sum\:of\:angles\:on\:a\:straight\:line\:=\:180°}$

➵ ∠ 2 + ∠ y = 180°

➵ 104.5° + ∠ y = 180°

➵ ∠ y = 180° - 104.5°

➵ ∠ y = 75.5°

Finally, we have

$\sf\pink{Sum\:of\:angles\:of\:a\:triangle\:=\:180°}$

⇢ ∠ 1 + 75.5° + 37.1° = 180°

⇢ ∠ 1 + 112.6° = 180°

⇢ ∠ 1 = 180° - 112.6°

⇢ ∠ 1 = 67.4°

$\boxed{Therefore,\:the\:measure\:of\:∠\:1\:is\:67.4°.}$

$\bold{ \green{ \star{ \orange{Hope\:it\:helps.}}}}⋆$