Question

in a triangle ABC the measure of angle A is 40 degrees less than the measure of angle B and 50 degrees less than that of angle C. find the measure of angle A

Answer 1

$\underline{\textsf{Given:}}$

$\textsf{In}\,\mathsf{\triangle\,ABC}$

$\mathsf{\angle{A}=\angle{B}-40^{\circ}}$

$\mathsf{\angle{A}=\angle{C}-50^{\circ}}$

$\underline{\textsf{To find:}}$

$\mathsf{\angle{A}}$

$\underline{\textsf{Solution:}}$

$\textsf{From the given information, we get}$

$\mathsf{\angle{B}=\angle{A}+40^{\circ}}$

$\mathsf{\angle{C}=\angle{A}+50^{\circ}}$

$\textsf{We know that, Sum of interior angles of a triangle is}\;\mathsf{180^{\circ}}$

$\implies\mathsf{\angle{A}+\angle{B}+\angle{C}=180^{\circ}}$

$\implies\mathsf{\angle{A}+\angle{A}+40^{\circ}+\angle{A}+50^{\circ}=180^{\circ}}$

$\implies\mathsf{3\,\angle{A}+90^{\circ}=180^{\circ}}$

$\implies\mathsf{3\,\angle{A}=180^{\circ}-90^{\circ}}$

$\implies\mathsf{3\,\angle{A}=90^{\circ}}$

$\implies\boxed{\mathsf{\angle{A}=30^{\circ}}}$

$\underline{\textsf{Answer:}}$

$\mathsf{\angle{A}=30^{\circ}}$

Answer 2

Step-by-step explanation:

Given:

\textsf{In}\,\mathsf{\triangle\,ABC}In△ABC

\mathsf{\angle{A}=\angle{B}-40^{\circ}}∠A=∠B−40

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\mathsf{\angle{A}=\angle{C}-50^{\circ}}∠A=∠C−50

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\underline{\textsf{To find:}}

To find:

\mathsf{\angle{A}}∠A

\underline{\textsf{Solution:}}

Solution:

\textsf{From the given information, we get}From the given information, we get

\mathsf{\angle{B}=\angle{A}+40^{\circ}}∠B=∠A+40

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\mathsf{\angle{C}=\angle{A}+50^{\circ}}∠C=∠A+50

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\textsf{We know that, Sum of interior angles of a triangle is}\;\mathsf{180^{\circ}}We know that, Sum of interior angles of a triangle is180

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\implies\mathsf{\angle{A}+\angle{B}+\angle{C}=180^{\circ}}⟹∠A+∠B+∠C=180

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\implies\mathsf{\angle{A}+\angle{A}+40^{\circ}+\angle{A}+50^{\circ}=180^{\circ}}⟹∠A+∠A+40

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+∠A+50

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=180

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\implies\mathsf{3\,\angle{A}+90^{\circ}=180^{\circ}}⟹3∠A+90

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=180

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\implies\mathsf{3\,\angle{A}=180^{\circ}-90^{\circ}}⟹3∠A=180

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−90

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\implies\mathsf{3\,\angle{A}=90^{\circ}}⟹3∠A=90

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\implies\boxed{\mathsf{\angle{A}=30^{\circ}}}⟹

∠A=30

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\underline{\textsf{Answer:}}

Answer:

\mathsf{\angle{A}=30^{\circ}}∠A=30

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