Question

6 fill in the blank 1 point when two straight lines intersect, angles opposite each other are called choose your answer... angles and they are choose your answer... angles that are next to each other (share a side) are called choose your answer... and they are choose your answer... 7 numeric 1 point find the missing measure. write your answer as a plain number: answer

Explanation:

Question 6

1. When two straight lines intersect, the angles opposite each other are vertical angles. By the vertical angles theorem, vertical angles are equal (congruent).
2. Angles that are next to each other (share a side) when two lines intersect are adjacent angles. These adjacent angles form a linear pair, so they are supplementary (their sum is \(180^\circ\)).

Step1: Identify the angle relationship

The diagram shows a right angle (marked with the red square), so the sum of the \(41^\circ\) angle and angle \(b\) is \(90^\circ\) (since they are complementary angles, adding up to a right angle).

Step2: Calculate angle \(b\)

We use the formula \(41^\circ + b = 90^\circ\). To find \(b\), we subtract \(41^\circ\) from \(90^\circ\).

$$ b = 90^\circ - 41^\circ $$

Step3: Perform the subtraction

$$ b = 49 $$

Answer:

First blank: vertical; Second blank: equal (or congruent); Third blank: adjacent angles; Fourth blank: supplementary (or their sum is \(180^\circ\))

Question 7