1.Given: Triangle PQR with m∠P=(2x)° , m∠Q=(4x)° , and m∠R=(6x)° .Prove: x = 15By the triangle sum theorem, the sum of the angles in a triangle is equal to 180°. Therefore, m∠P+m∠Q+m∠R=180° . Using the ,__________ (2x)°+(4x)°+(6x)°=180° . Simplifying the equation gets 12x = 180. Finally, using the division property of equality, .___________answer to each box to completesubstitution property, distributive property, angle addition postulate, x=12 x=15 x=30

we havem∠P=[tex](2x)\°[/tex]m∠Q=[tex](4x)\°[/tex]m∠R=[tex](6x)\°[/tex]1) By the triangle sum theorem, the sum of the angles in a triangle is equal to [tex]180\°[/tex]thereforem∠P+m∠Q+m∠R=[tex]180\°[/tex]we know thatSubstitution Property of Equality, states that If the values of two quantities are known to be equal, you can replace the value of one quantity with the otherso2) Using the Substitution Property of Equality[tex](2x)\°+(4x)\°+(6x)\°=180\°[/tex]Simplifying the equation gets[tex](12x)\°=180\°[/tex]3) using the division property of equalityThe Division Property of Equality states that if you divide both sides of an equation by the same nonzero number, the sides remain equal[tex](12x)\°/12=180\°/12[/tex] [tex]x=15\°[/tex]thereforethe answer isPart a) Substitution Property of EqualityPart b)  [tex]x=15\°[/tex]