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Triangles — MATHS STD 9 — Question

Rajasthan BoardEnglish MediumSTD 9MATHSTriangles1 Mark
Question
In a $\triangle\text{ABC},$ if $\angle\text{A}−\angle\text{B}=42^\circ$ and $\angle\text{B}−\angle\text{C}=21^\circ$ then $\angle\text{B} = ?$
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Answer

  1. 53º
    Solution:
    Let,
    $\angle\text{A}−\angle\text{B}=42°...\ \text{(i)}$ and
    $\angle\text{B}−\angle\text{C}=21^\circ ...\ \text{(ii)}$
    Adding (i) and (ii),we get
    $\angle\text{A}−\angle\text{C}=63° ...\ \text{(iii)}$
    $\angle\text{B}=\angle\text{A}−42^\circ$ [using (i)]
    $\angle\text{C}=\angle\text{A}−63^\circ$ [Using (iii)]
    $∴\angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ$ [Sum of the angles of a triangle]
    $⇒\angle\text{A}+\angle\text{A}−42^\circ+\angle\text{A}−63^\circ=180^\circ$
    $⇒3\angle\text{A}−105^\circ=180^\circ$
    $⇒3\angle\text{A}=285^\circ$
    $∴\angle\text{B}=(95−42)^\circ$
    $⇒\angle\text{B}=53^\circ$

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