Answer and Step-by-step explanation:
25. We know that the 4 angles in a quadrilateral add up to 360°.
To find the first angle, we need to first add all of the ratios together.
1 + 2 + 3 + 4 = 10.
Divide 360 by 10 to get the measure of angle 1.
∠1 = 360 ÷ 10 = 36°
Now, we multiply the first angle by the ratios to get the corresponding angles.
∠2 = 36 × 2 = 72°
∠3 = 36 × 3 = 108°
∠4 = 36 × 4 = 144°
We can confirm that these angles are correct by adding them together and checking to see if they are equal to 360°.
36 + 72 + 108 + 144 =
108 + 108 + 144 =
216 + 144 =
360
This is your answer.
∠A = 36°
∠B = 72°
∠C = 108°
∠D = 144°
We aren't done yet, as there is a second part to the question. The question asks to determine which segments of the quadrilateral are parallel.
In the attached picture, the quadrilateral could look something like this (A Trapezoidal Shape). 2 of the angles have to be less than 90°, and 2 of the angles have to be more than 90°. All 4 angles can't be equal to each other or look exactly the same, as determined by the angle measurements we found.
By looking at the picture, we can see that line segment AB is parallel to line segment CD, and this occurred due to the bottom two angles of the trapezoid being angles less than 90°, and the top two angles of the trapezoid being angles more than 90°.
So, the segments that are parallel to each other are segments AB and CD.
Have a great day!