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kokilavani

26.01.2023

Mathematics

$x^{\circ}=56^{\circ};$

The exterior angle has measure $116^{\circ}.$

Step-by-step explanation:

Angle QRP and angle with measure of (2x+4)° are supplementary, then

$m\angle QRP+(2x+4)^{\circ}=180^{\circ},\\ \\m\angle QRP=180^{\circ}-(2x+4)^{\circ}.$

The sum of the measures of all interior angles of the triangle is equal to 180°, then

$m\angle PQR+m\angle QRP+m\angle RPQ=180^{\circ},\\ \\x^{\circ}+180^{\circ}-(2x+4)^{\circ}+60^{\circ}=180^{\circ},\\ \\x^{\circ}-2x^{\circ}=-60^{\circ}+4^{\circ},\\ \\-x^{\circ}=-56^{\circ},\\ \\x^{\circ}=56^{\circ}.$

The exterior angle has measure

$(2\cdot 56+4)^{\circ}=116^{\circ}.$

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