The exterior angle obtained on producing the base of a triangle both ways or hundred degree and 120° . find all the angles. You can also write the answer in a sheet of paper and send the picture . that’s enough
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The exterior angle obtained on producing the base of a triangle both ways or hundred degree and 120° . find all
Verified answer
Explanation:
Let the triangle be ABC and BC be extended to DE, such that
ABD = 100°, and ∠ACE = 120°.
Angles ABD and ACE form a linear pair. Hence,
[tex]\mathsf{ABD + ABC=180}[/tex]
[tex]\mathsf{==>100+ABC=180}[/tex]
[tex]\mathsf{==> ABC = 180-100}[/tex]
∴ ∠ABC = 80°
Similarly, ∠ACE and ∠ACB form a linear pair, and so,
[tex]\mathsf{ACE+ACB=180}[/tex]
[tex]\mathsf{==>120+ACB=180}[/tex]
[tex]\mathsf{==> ACB=180-120}[/tex]
∴ ∠ACB = 60°
By the angle sum property of a triangle, we know that
[tex]\mathsf{ABC + ACB + BAC=180}[/tex]
[tex]\mathsf{==> 80+60+BAC=180}[/tex]
[tex]\mathsf{==>BAC=180-140}[/tex]
∴ ∠BAC = 40°
Hence, the angles of the triangle are 40°, 60° and 80°.
Answer: 40°, 60°, 80°
I hope this helps. :D