Question

write an algebraic expression for each quantity. 2.7 43. the second angle of a linear pair if the first angle has a measure of x° 44. the complement of an angle with a measure of (x + 23)°

Explanation:

43.

Step1: Recall the property of linear - pair angles

The sum of angles in a linear pair is \(180^{\circ}\). Let the first angle be \(x^{\circ}\) and the second angle be \(y^{\circ}\). Then \(x + y=180\).

Step2: Solve for \(y\)

Subtract \(x\) from both sides of the equation \(x + y = 180\). We get \(y=180 - x\).

44.

Step1: Recall the property of complementary angles

The sum of complementary angles is \(90^{\circ}\). Let the given angle be \(A=(x + 23)^{\circ}\) and its complement be \(B\). Then \(A + B=90\).

Step2: Solve for \(B\)

Substitute \(A=(x + 23)\) into \(A + B=90\). We have \((x + 23)+B = 90\). Subtract \((x + 23)\) from both sides:

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Answer:

1. The algebraic expression for the second angle of the linear pair is \(180 - x\).
2. The algebraic expression for the complement of the angle \((x + 23)^{\circ}\) is \(67 - x\).