In 🔺 PQR, if angle P - angle Q = 42° and angle Q - angle R =21°.Find angle P, angle Q and angle R

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Solution

GIVEN :
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In Δ PQR

angleP - angleQ=42°
angleP=42°+ angleQ--------(i)

angleQ-angleR=21°
angleR=angleQ - 21----------(ii)

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BY USING ANGLE SUM PROPERTY :

angleP+angleQ+angleR=180°

[Using values of angleP and angleR from eq(i) and eq(ii) respectively ]

42+angleQ+angleQ+angleQ-21=180

3angleQ+21=180

3angleQ=180-21

3angleQ=159

angleQ=159/3

angleQ=53

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From eq(i)

angleP=42+angleQ
angleP=42+53
angleP=95

From eq(ii)

angle R=angleQ-21
angleR=53-21
angleR=32

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MEASURE OF ALL THE ANGLES:

angleP=95°
angleQ=53°
angleR=32°

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