Question

1 ∠4 and ∠7 form a linear pair definition of linear pair
2 ∠4 and ∠7 are supplementary definition of linear pair
3 ∠4 ≅ ∠6 given
4 ∠7 ≅ ∠6 vertical angles property
5 ∠0 ≅ ∠0 transitive property
6 ∠4 and ∠7 are right angles if two angles are congruent and supplementary, then they are right angles

Explanation:

Step1: Recall the transitive property

The transitive property states that if \(a = b\) and \(b = c\), then \(a = c\). In terms of congruent angles, if \(\angle x\cong\angle y\) and \(\angle y\cong\angle z\), then \(\angle x\cong\angle z\).

Step2: Identify the congruent angles from previous steps

From step 2, \(\angle4\cong\angle6\) (given) and from step 4, \(\angle7\cong\angle6\).

Step3: Apply the transitive property

By the transitive property of congruent angles, if \(\angle4\cong\angle6\) and \(\angle7\cong\angle6\), then \(\angle4\cong\angle7\)

Answer:

\(\angle4\cong\angle7\)