Question

for exercises 1 - 6, find the value of each variable. 1. 92° 63° x° 2. 20° 87° x°

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 the first triangle

For the first triangle with angles 92°, 63°, and \(x\), we have the equation \(92 + 63+x=180\).
Combining like - terms: \(155 + x=180\).
Subtracting 155 from both sides: \(x=180 - 155\).
\(x = 25\).

Step3: Solve for x in the second triangle

For the second triangle, we know one angle is 20° and another is 87°, and the sum of the interior angles is 180°. So the equation is \(20+87 + x=180\).
Combining like - terms: \(107+x=180\).
Subtracting 107 from both sides: \(x=180 - 107\).
\(x = 73\).

Answer:

1. \(x = 25\)
2. \(x = 73\)