Question

What is the sum of the measures of the interior angles at vertex \(i\) and vertex \(j\)?

a) 128°
b) 142°
c) 52°
d) 38°

Answer 1

The sum of the measures of the interior angles at vertex i and vertex j can be found by doubling the difference between the measures of the interior angles at the two vertices.

Step-by-step explanation:

The sum of the measures of the interior angles at vertex i and vertex j can be found using the following steps:

1. Find the measure of the interior angle at vertex i (denoted as 0₁) using the given information. In this case, 0₁ = (2)(14.5°) = 29°.
2. Find the difference between the measure of the interior angle at vertex j (denoted as 0₂) and 0₁. In this case, 0₂ - 0₁ = 30.05° - 14.5° = 15.56°.
3. Double the value of the difference obtained in the previous step. In this case, (2)(15.56°) = 31.1°.

Therefore, the sum of the measures of the interior angles at vertex i and vertex j is approximately 31.1°.