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

Given all four angles of a quadrilateral. Sum of all angles of a quadrilateral is equal to 360°.

So, m<A+ m<B+m<C + m <D = 360°.

7x+5x+7x+5x= 360 (Substitution property).

24x = 360 (Combine like terms).

x= 15 (Proved)

Answer 2

Explanation:

Statements Reasons

1. Quadrilateral ABCD with m∠A = (7x)° Given

m∠B = (5x)°, m∠C = (7x)° and m∠D = ( 5x)°

2. m∠A + m∠B + m∠C + m∠D = 360° The sum of the interior angle

of the quadrilateral is 360°

3. (7x)° + (5x)° + (7x)° + (5x)° = 360° Substitution property

4. 24x = 360 Combine like terms

5. x = 15 Division property of equality