measure of angles marked with letters - Maths - The Triangle and its Properties

Question

measure of angles marked with letters

Shruti Tyagi · Accepted Answer

Dear Student,

∠PRQ=∠SRT=42°   Vertically opposite anglesin △PRQSum of 3 angles of triangle=180∠RPQ+∠PRQ+∠RQP=180⇒45+42+z=180⇒z=180-87⇒z=93°now z+y=180   PQ is a straight line and angle z and y form a linear pair⇒93+y=180⇒y=180-93⇒y=87°in △SRTsince x is interior angle of triangle∠SRT+∠RST=x  exterior angle of a triangle is equal to sum of interior opposite angles⇒100+42=x⇒x=142°

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