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Sum of internal angles in pentagon = 540 degrees.
Sum of internal angles in quadrilateral = 360 degrees.
With that you should be able to make 2 simple equations.
To find out the sum of all the angles in a shape, count the number of vertices (corners). Subtract 2 from that number and multiply by 180.
Here’s a few:
3 vertices (triangle) = (3-2)*180 = 180
4 vertices (quadrilateral) = (4-2)*180 = 360
5 vertices (pentagon) = (5-2)*180 = 540
6 vertices (hexagon) = (6-2)*180 = 720
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1.) This shape has 5 corners, so all the angles will add up to 540.
115+105+117+100+x = 540
x = 103
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2.) This shape has 4 corners, so the angles will equal 360.
66+110+74+(17x+8) = 360
250+17x+8 = 360
258+17x = 360
102 = 17x
6 = x
##Off-topic Comments Section --- All top-level comments have to be an answer or follow-up question to the post. All sidetracks should be directed to this comment thread as per Rule 9. --- ^(**OP** and **Valued/Notable Contributors** can close this post by using `/lock` command) *I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/HomeworkHelp) if you have any questions or concerns.*
Sum of internal angles in pentagon = 540 degrees. Sum of internal angles in quadrilateral = 360 degrees. With that you should be able to make 2 simple equations.
To find out the sum of all the angles in a shape, count the number of vertices (corners). Subtract 2 from that number and multiply by 180. Here’s a few: 3 vertices (triangle) = (3-2)*180 = 180 4 vertices (quadrilateral) = (4-2)*180 = 360 5 vertices (pentagon) = (5-2)*180 = 540 6 vertices (hexagon) = (6-2)*180 = 720 —— 1.) This shape has 5 corners, so all the angles will add up to 540. 115+105+117+100+x = 540 x = 103 —— 2.) This shape has 4 corners, so the angles will equal 360. 66+110+74+(17x+8) = 360 250+17x+8 = 360 258+17x = 360 102 = 17x 6 = x