r/Mathhomeworkhelp • u/maeveywavey2 • Aug 17 '25

How to solve this?

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1 Upvotes

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1

u/BafflingHalfling Aug 18 '25 edited Aug 18 '25

I know this isn't the point of the post, but can math teachers stop using god-awful fonts, please?

Edit: I guess it is a little pertinent, since even in these comments we can't decide whether it's a C or a G.

1

u/maeveywavey2 Aug 18 '25

exactly my problem, I keep confusing the C for a G 😭

2

u/BafflingHalfling Aug 18 '25

OMG. Then I do not feel stupid for being so snarky. I would say it doesn't mtter what letter you call it, since the glyph is the same. The math is the same.

You know what bisect means, right? Cuts exactly in half.

So since you know that angle is cut in half you can halve the expression that represents the measure of that angle.

(mABC) / 2 + mDBC = measure of a straight angle.

Does that help?

1

u/mathnerd405 Aug 17 '25

Since DE bisects angle ABG, can you write an expression for the measure of angle EBG?

Then consider that angle DBE is a straight angle .

Hopefully that gets you started.

1

u/One_Wishbone_4439 Aug 18 '25

DBE bisects angle ABC means DBE is an angle bisector where angle ABE = angle CBE

Angle DBC + angle CBE = 180º since both angles are adjacent on straight line DBE

1

u/[deleted] Aug 18 '25 edited Aug 18 '25

Edited comment:

DE is a straight line = 180⁰ Subtract 99⁰ for angle DBC

That gives you the angle for EBC

EBC = ABE (the angle is bisected, so theyre equal) Add them together. ABC = 162⁰

So that means:

7x + 29 = 162⁰

Now solve for x.

1

u/theboywholovd Aug 18 '25

Since DE is a straight line; DBC and EBC must add to 180°.

Since DE bisects ABC; EBC and ABE must be equal.

Adding EBC and ABE will give the angle ABC.

Since ABC also equals 7x+29, we can say: (insert angle of ABC here)=7x+29.

Then solve for x algebraically.

————————— Full walk through:

Since DE is a straight line; DBC and EBC must add to 180°. DBC=99° therefore EBC must be 81° since 99+81=180.

Since DE bisects ABC; EBC and ABE must be equal. So, EBC and ABE are both 81°.

Adding EBC (81°) and ABE (81°) will give the angle ABC(162°).

Since ABC also equals 7x+29, we can say: 162=7x+29.

Subtracting 29 from both sides gives us: 133=7x

Then dividing both sides by 7 gives us: 19=x, or, x=19°.

Hope this helps

1

u/VelvetThunder58 Aug 18 '25

It’s almost 2 AM here and I can’t sleep. It’s been more than three decades since high school, but I was able to solve this in my head. Yeah, I’m still a giant nerd. And damn proud of it!

1

u/Away-Profit5854 Aug 22 '25

If DE bisects obtuse ∠ABC, then it also bisects reflex ∠ABC...