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The measures of ∠ 1 and ∠ 2.
[tex]{\boxed{\mathcal{\red{Angle\: 1 \:=\: 67.4° \:}}}}[/tex]✅
[tex]{\boxed{\mathcal{\red{Angle\: 2\:=\:104.5° \:}}}}[/tex]✅
We know that,
[tex]\sf\purple{Sum\:of\:angles\:on\:a\:straight\:line\:=\:180°}[/tex]
✒ ∠ x + 121.8° = 180°
✒ ∠ x = 180° - 121.8°
✒ ∠ x = 58.2°
Now,
[tex]\sf\pink{Sum\:of\:angles\:of\:a\:triangle\:=\:180°}[/tex]
➪ ∠ 2 + 17.3° + 58.2° = 180°
➪ ∠ 2 + 75.5° = 180°
➪ ∠ 2 = 180° - 75.5°
➪ ∠ 2 = 104.5°
[tex]\boxed{Therefore,\:the\:measure\:of\:∠\:2\:is\:104.5°.}[/tex]
Again,
[tex]\sf\blue{Sum\:of\:angles\:on\:a\:straight\:line\:=\:180°}[/tex]
➵ ∠ 2 + ∠ y = 180°
➵ 104.5° + ∠ y = 180°
➵ ∠ y = 180° - 104.5°
➵ ∠ y = 75.5°
Finally, we have
[tex]\sf\pink{Sum\:of\:angles\:of\:a\:triangle\:=\:180°}[/tex]
⇢ ∠ 1 + 75.5° + 37.1° = 180°
⇢ ∠ 1 + 112.6° = 180°
⇢ ∠ 1 = 180° - 112.6°
⇢ ∠ 1 = 67.4°
[tex]\boxed{Therefore,\:the\:measure\:of\:∠\:1\:is\:67.4°.}[/tex]
[tex]\bold{ \green{ \star{ \orange{Hope\:it\:helps.}}}}⋆[/tex]
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Rewritten by : Barada
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
If my answer is incorrect, pls correct me!
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-Chetan K
