Question

ca cc 8.ee.7, 8.ee.7b, 8.g.5
find the measure of each angle.
8.
m∠e =
m∠f =
10.
m∠g =
m∠h =
m∠j =

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°.

Step2: Solve for \(x\) in \(\triangle DEF\)

In \(\triangle DEF\), we have \(x + x+98 = 180\). Combining like - terms gives \(2x+98 = 180\). Subtract 98 from both sides: \(2x=180 - 98=82\). Then divide by 2: \(x = 41\).
So \(m\angle E=x = 41^{\circ}\) and \(m\angle F=x = 41^{\circ}\).

Step3: Solve for \(x\) in \(\triangle GHJ\)

In \(\triangle GHJ\), we have \(4x + 3x+5x = 180\). Combining like - terms gives \(12x = 180\). Divide both sides by 12: \(x = 15\).
Then \(m\angle G = 5x=5\times15 = 75^{\circ}\), \(m\angle H = 4x=4\times15 = 60^{\circ}\), \(m\angle J = 3x=3\times15 = 45^{\circ}\).

Answer:

For \(\triangle DEF\):
\(m\angle E = 41^{\circ}\)
\(m\angle F = 41^{\circ}\)
For \(\triangle GHJ\):
\(m\angle G = 75^{\circ}\)
\(m\angle H = 60^{\circ}\)
\(m\angle J = 45^{\circ}\)