Question

which property/postulate needs to be used for the blank in the paragraph proof? given: triangle pqr with (mangle p=(2x)^{circ},mangle q=(4x)^{circ}) and (mangle r=(6x)^{circ}) prove: (x = 15) by the triangle sum theorem, the sum of the angles in a triangle is equal to (180^{circ}). therefore, (mangle p+mangle q+mangle r = 180^{circ}). using the ____________. ((2x)^{circ}+(4x)^{circ}+(6x)^{circ}=180^{circ}). simplifying the equations gets (12x = 180^{circ}). finally using the division property of equality, (x = 15). angle addition postulate distributive property division property of equality substitution property

Explanation:

We know that since \(m\angle P=(2x)^{\circ}\), \(m\angle Q=(4x)^{\circ}\) and \(m\angle R=(6x)^{\circ}\), and \(m\angle P + m\angle Q + m\angle R=180^{\circ}\), we substitute the values of the angles into the equation. The substitution property allows us to replace a quantity with its equal in an equation. Here we replace \(m\angle P\), \(m\angle Q\) and \(m\angle R\) with their respective expressions in terms of \(x\).

Answer:

D. substitution property