Question

1 complete the activity below, answering all of the questions.
2 when you have finished the guided practice activity, upload a screenshot of your score screen to earn credit for this activity.
challenge #1
fill in the missing words
to help find the measure of angle 1, 2 and y we need to
notice the angle relationships. the first angle relationship
we notice is angles which we know are
(i.e. equal in measure). the other angle
relationship is the of the angles of a
triangle. we know that if we add all the angles in a triangle
they will add to degrees

Explanation:

Step1: Find the measure of angle 1

We know that the sum of angles in a triangle is \(180^{\circ}\). For the left - hand triangle with angles \(19^{\circ}\), \(41^{\circ}\), and angle 1.
Using the formula \(\text{Sum of angles in a triangle}=180^{\circ}\), we have \(19^{\circ}+41^{\circ}+\angle1 = 180^{\circ}\).

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Step2: Use the vertical - angle relationship

Angle 1 and angle 2 are vertical angles. Vertical angles are equal in measure. So \(\angle2=\angle1 = 120^{\circ}\)

Step3: Find the measure of angle Y

For the right - hand triangle with angles \(38^{\circ}\), \(\angle2 = 120^{\circ}\), and \(Y\).
Using the formula \(\text{Sum of angles in a triangle}=180^{\circ}\), we have \(38^{\circ}+120^{\circ}+Y = 180^{\circ}\)

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Step4: Fill in the blanks

The angle relationship for \(\angle1\) and \(\angle2\) is that they are vertical angles (equal in measure). The other angle relationship is the sum of the angles of a triangle (they will add to \(180\) degrees)

Answer:

The blanks are filled as follows:

• The first blank (angle relationship for \(\angle1\) and \(\angle2\)): vertical
• The second blank: sum
• The third blank: triangle
• The fourth blank: \(180\)