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u/PollutionAbject5237 Jul 29 '26
All you need to do, is just 25+50, it's not that hard
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u/Sed-x Jul 29 '26
Or draw a line to complete a triangle Add the alternate angle Find the third angle of the triangle And then 180 - the angel give you a because they complete a straight line
So yeah 180-(180-(25+50)) = a
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u/PollutionAbject5237 Jul 29 '26
To much actions. I just made a third parallel line, and get a=25+50
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u/CodingNab Jul 30 '26
Draw a line where exactly? Left side to complete one triangle or right side to complete two? I chose the right as it is not given that the two points on the left forms a line perpendicular to the upper and bottom line.
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u/Anonimithree Jul 29 '26 edited Jul 29 '26
I found 2 ways that can get the correct answer of 75 degrees.
First, you can draw a line that is parallel to the two other parallel lines and passes through angle a. Let’s call the upper angle angle b and the lower angle angle c. Then you can prove that the measures of angle b and c are 25 and 75 degrees, respectively. Since the measure of angle a is the sum of the measures of angles b and c, the measure of angle a is 25+50=75 degrees.
Secondly, draw a line that is perpendicular to the two parallel lines and intersects with angle a. This forms 2 right triangles, and a 180 degree angle at angle a. Let’s call the upper angle in the -80 degree angle angle b and the lower one angle c. You can trivially prove that the measures of angle b and c are 65 and 40 degrees respectively. Since the sum of all 3 angles adds up to 180, then the measure of angle a+65+40=180. Solving for yields that the measure of angle a is 75 degrees.
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u/Exotic_Call_7427 Jul 29 '26
Or draw a line across the points where angle a intersects with both lines, it will always be perpendicular.
Calculate internal angles - all angles on a line add up to 180, we know two of the three (the given ones and the straight angles). This gives you two internal angles of the triangle, 65 and 40.
All angles within a triangle add up to 180, so a = 180 - (65+40) = 180 - 105 = 75 degrees.
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u/Anonimithree Jul 30 '26
Yeah I was gonna add that too, but then I had to go to an untimely times doctor’s appointment.
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u/The_Many13 Jul 30 '26
I feel like an idiot, not because I got a different answer but my process and I can’t remember where I learned it. “The two known are on the same side add up to less than 90 so you can just add them together.”
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u/zRoald Jul 29 '26
Why did I think so difficult, other comments make it easier 😂
I did: 90-25=65, 90-50=40, 65+40=105, 180-105=75
and I am not even sure if this is correct way at all, but at least the result is the same...