Question

consider the angles formed by the garden gate. what can be concluded from each of the following statements? state the theorem that yields each conclusion.
a. m∠1 = 90 and m∠2 = 90.
b. ∠3 and ∠4 are vertical angles.
a. given that m∠1 = 90 and m∠2 = 90, what can be concluded?
a. it can be concluded that ∠1≅∠2 since all right angles are congruent.
b. it can be concluded that ∠1 and ∠2 are complementary angles by the definition of complementary angles.
c. it can be concluded that ∠1≅∠2 since vertical angles are congruent.
d. it can be concluded that m∠1 + m∠2 = 180 since the sum of the measures of a linear pair is 180.

Explanation:

Step1: Recall angle - congruence rules

All right - angles have a measure of 90 degrees. If two angles have the same measure, they are congruent.

Step2: Analyze given angle measures

Given \(m\angle1 = 90\) and \(m\angle2=90\), \(\angle1\) and \(\angle2\) are right - angles. Since all right - angles are congruent, \(\angle1\cong\angle2\).

Answer:

A. It can be concluded that \(\angle1\cong\angle2\) since all right angles are congruent.