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.
b. it can be concluded that ∠1 and ∠2 are complementary angles by the definition of complementary angles.
c. it can be concluded that m∠1 + m∠2 = 180 since the sum of the measures of a linear pair is 180.
d. it can be concluded that ∠1≅∠2 since all right angles are congruent.
b. given that ∠3 and ∠4 are vertical angles, what can be concluded?
a. it can be concluded that ∠3 and ∠4 are complementary angles by the definition of complementary angles.
b. it can be concluded that ∠3≅∠4 since all vertical angles are right angles and all right angles are congruent.
c. it can be concluded that ∠3≅∠4 since vertical angles are congruent.
d. it can be concluded that m∠3 + m∠4 = 180 since the sum of the measures of a linear pair is 180.

Explanation:

Step1: Analyze part a

Given \(m\angle1 = 90\) and \(m\angle2=90\). Right - angles are congruent. So \(\angle1\cong\angle2\).

Step2: Analyze part b

Vertical angles are congruent. Given \(\angle3\) and \(\angle4\) are vertical angles, so \(\angle3\cong\angle4\).

Answer:

a. D. It can be concluded that \(\angle1\cong\angle2\) since all right angles are congruent.
b. C. It can be concluded that \(\angle3\cong\angle4\) since vertical angles are congruent.