Question

Drag a statement or reason to each box to complete this proof.

Given: Quadrilateral ABCD with m∠A=(7x)° , m∠B=(5x)° , m∠C=(7x)° , and m∠D=(5x)° .

Prove: x = 15

Answer 1

2.

Statement

m∠A + m∠B + m∠C + m∠D = 360°

Reason

The sum of interior angles of a quadrilateral is 360°

3.

Statement

(7x)° + (5x)° + (7x)° + (5x)° = 360°

Reason

Substitution property

4.

Statement

24x = 360

Reason

Combine like terms

Answer 2

In the given quadrilateral ABCD,

`m\angle A=7x^(\circ) , m\angle B=5x^(\circ), m\angle C=7x^(\circ) , m\angle D=5x^(\circ) (Given)`

`m\angle A + m\angle B+ m\angle C+ m\angle D=360^(\circ)`

(Sum of interior angles of a quadrilateral is 360 degrees)

`7x\dot{^(\circ)} + 5x^(\circ)+ 7x\dot{^(\circ)} + 5x^(\circ)=360^(\circ)`(Substitution Property)

`24x^(\circ)=360\dot{^(\circ)}` (Addition Property of Equality)

`x=15^(\circ)`