Question

1. what type of angles are in the diagram, select all that apply:

a adjacent
b complementary
c supplementary
d vertical
find their measures by creating and solving the equation:

Explanation:

Step1: Determine the type of angles

Adjacent angles share a common side and vertex. Complementary angles sum to \(90^{\circ}\). In the diagram, the two angles \((3a - 1)^{\circ}\) and \((6a - 5)^{\circ}\) share a common side and vertex (adjacent) and their sum is \(90^{\circ}\) (complementary as there is a right - angle symbol).

Step2: Create the equation

Since the angles are complementary, \((3a - 1)+(6a - 5)=90\).
Simplify the left - hand side: \(3a-1 + 6a-5=9a-6\). So, \(9a - 6=90\).
Add \(6\) to both sides: \(9a-6 + 6=90 + 6\), which gives \(9a=96\).
Divide both sides by \(9\): \(a=\frac{96}{9}=\frac{32}{3}\).

Step3: Find the measures of the angles

For the first angle \((3a - 1)^{\circ}\), substitute \(a = \frac{32}{3}\):
\(3\times\frac{32}{3}-1=32 - 1=31^{\circ}\).
For the second angle \((6a - 5)^{\circ}\), substitute \(a=\frac{32}{3}\):
\(6\times\frac{32}{3}-5=64 - 5=59^{\circ}\).

Answer:

A. Adjacent, B. Complementary. The measures of the angles are \(31^{\circ}\) and \(59^{\circ}\).