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lets see if you are capable of making me hard jff-hiyr-cuu
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Jo.in Hèré [qyf-axun-jjf]
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If one of the angles of a triangle is 130∘ then the angle between the bisectors of the other two angles can be a 50∘ b 65∘ c 90∘ d 155∘
Solution
ANSWER:
Let △ABCbesuchthat∠A=130∘
Here, BP is the bisector of ∠BandCPisthebisectorof∠C.
∴ ∠ABP=∠PBC=1/2∠B .....(1)
Also, ∠ACP=∠PCB=1/2∠C
.....(2)In △ABC,
∠A+∠B+∠C=180∘ (Angle sum property)
⇒ 130∘+∠B+∠C=180∘
⇒ ∠B+∠C=180∘−130∘=50∘
⇒ 1/2 ∠B+1/2∠C=1/2×50∘=25∘
⇒ ∠PBC+∠PCB=25∘ .....(3) [Using (1) and (2)]
In △PBC,
∠PBC+∠PCB+∠BPC=180∘
⇒25∘+∠BPC=180∘ (Angle sum property) [Using (3)]
⇒ ∠BPC=180∘−25∘=155∘
Thus, if one of the angles of a triangle is 130∘thentheanglebetweenthebisectorsoftheothertwoanglesis155∘.
Hence, the correct answer is option (d).
Mathematics
Secondary School Mathematics IX
Standard IX
7