Question

1. the measure of an angle is 75°. what is the measure of its complementary angle?

a. 15° b. 25° c. 75° d. 105°

1. a diagram is shown below.

diagram with points a, b, c, d, e, f, g; right angle at g between some lines
which angle must be congruent to ∠agb?
a. ∠dge b. ∠ega c. ∠agf d. ∠cgd

1. what is the supplement of a 40° angle?

a. 50° b. 130° c. 140° d. 220°

Explanation:

Question 5

Step1: Recall complementary angle definition

Complementary angles sum to \(90^\circ\).

Step2: Calculate the complementary angle

Let the complementary angle be \(x\). Then \(75^\circ + x = 90^\circ\). Solving for \(x\), we get \(x = 90^\circ - 75^\circ = 15^\circ\).

To determine which angle is congruent to \(\angle AGB\), we analyze vertical angles or right angles. From the diagram, \(\angle AGB\) and \(\angle DGE\) are vertical angles (or can be shown to be congruent via right angle and vertical angle properties). \(\angle EGA\) is a straight - like or different - measure angle, \(\angle AGF\) is not congruent, and \(\angle CGD\) is also not congruent.

Step1: Recall supplement angle definition

Supplementary angles sum to \(180^\circ\).

Step2: Calculate the supplementary angle

Let the supplementary angle be \(y\). Then \(40^\circ + y = 180^\circ\). Solving for \(y\), we get \(y = 180^\circ - 40^\circ = 140^\circ\).

Answer:

A. \(15^\circ\)

Question 6