Question

1. finding supplements in the table, assume that ∠1 and ∠2 are supplementary. copy and complete the table.

m∠1	4°	16°	48°	72°	90°	99°	120°	152°	169°	178°
m∠2	?	?	?	?	?	?	?	?	?	?

Explanation:

Supplementary angles are two angles whose sum is \(180^\circ\). So, to find \(m\angle2\) when \(m\angle1\) is given, we use the formula \(m\angle2 = 180^\circ - m\angle1\).

Step 1: For \(m\angle1 = 4^\circ\)

We know that supplementary angles sum to \(180^\circ\). So we subtract \(m\angle1\) from \(180^\circ\) to find \(m\angle2\).
\(m\angle2 = 180^\circ - 4^\circ = 176^\circ\)

Step 2: For \(m\angle1 = 16^\circ\)

Using the same formula for supplementary angles.
\(m\angle2 = 180^\circ - 16^\circ = 164^\circ\)

Step 3: For \(m\angle1 = 48^\circ\)

Subtract \(48^\circ\) from \(180^\circ\).
\(m\angle2 = 180^\circ - 48^\circ = 132^\circ\)

Step 4: For \(m\angle1 = 72^\circ\)

Subtract \(72^\circ\) from \(180^\circ\).
\(m\angle2 = 180^\circ - 72^\circ = 108^\circ\)

Step 5: For \(m\angle1 = 90^\circ\)

Subtract \(90^\circ\) from \(180^\circ\).
\(m\angle2 = 180^\circ - 90^\circ = 90^\circ\)

Step 6: For \(m\angle1 = 99^\circ\)

Subtract \(99^\circ\) from \(180^\circ\).
\(m\angle2 = 180^\circ - 99^\circ = 81^\circ\)

Step 7: For \(m\angle1 = 120^\circ\)

Subtract \(120^\circ\) from \(180^\circ\).
\(m\angle2 = 180^\circ - 120^\circ = 60^\circ\)

Step 8: For \(m\angle1 = 152^\circ\)

Subtract \(152^\circ\) from \(180^\circ\).
\(m\angle2 = 180^\circ - 152^\circ = 28^\circ\)

Step 9: For \(m\angle1 = 169^\circ\)

Subtract \(169^\circ\) from \(180^\circ\).
\(m\angle2 = 180^\circ - 169^\circ = 11^\circ\)

Step 10: For \(m\angle1 = 178^\circ\)

Subtract \(178^\circ\) from \(180^\circ\).
\(m\angle2 = 180^\circ - 178^\circ = 2^\circ\)

Answer:

\(m\angle1\)	\(4^\circ\)	\(16^\circ\)	\(48^\circ\)	\(72^\circ\)	\(90^\circ\)	\(99^\circ\)	\(120^\circ\)	\(152^\circ\)	\(169^\circ\)	\(178^\circ\)