Lazy Pizza Parlor

Geometry Level 1

You order a pizza from a parlor with some friends. The chef has cut the round pie into four slices with two straight cuts that go through the center of the pizza. One of the slices is three times as large as the piece just next to it! What's the angle of the tip of the largest pizza slice in the box?

145^{\circ}

90^{\circ}

135^{\circ}

There's not enough information to know

120^{\circ}

3 solutions

A Former Brilliant Member
Jul 17, 2017

Note that if one slice is three times as large as the other, the central angle is also three times as large as the other. Let $x$ be the central angle of the smallest slice then the central angle of the largest slice must be $3x$ . In the problem, it says that the smallest slice is next to the largest slice. We know that vertical angles are equal and one revolution is $360^\circ$ , so from my figure, we have

$x+3x+x+3x=360$

$8x=360$

$x=45$

Finally,

$3x=3(45)=$ $\boxed{\color{#D61F06}\large 135^\circ}$

Good solution. Exactly as I solved it.

David Brown - 1 year, 9 months ago

Eli Ross Staff
Oct 2, 2015

Because there are two cuts, the sum of the angles at the tip of these two slices must be supplementary angles and thus sum to $180^\circ.$ However, the area of the slice is proportional to the angle, so we have $3x + x = 180^\circ,$ so $3x=135^\circ.$

We know this must be the largest slice, since the other two slices must also have angles $135^\circ,45^\circ$ since they form vertical angles .

Bt there haven't enough information

Nasifur Niloy - 5 years, 6 months ago

Why??? Plz explain in detail

Ashish Menon - 5 years, 1 month ago

135 plus 45 is only 180 not 190.

John Wiggin - 4 years, 10 months ago

If one tip is 135°, the one vertically opposite to it is also 135°. So, that covers 135+135 = 270° portion of the pizza. What remains is 360 - 270 = 90° which xan be equally divided into 45° slices. As we can observe $135 = 3 × 45$ , so our answer is $\color{#3D99F6}{\boxed{{135}^°}}$ .

Ashish Menon - 4 years, 10 months ago

similar to others 3x+3x+x+x=360 x=45 3x=135 Why? I don't want to get into it. My math is rusty.

Danny Peltier - 4 years, 10 months ago

Ashish Menon - 4 years, 10 months ago

That's not the correct answer!!!!!!!!!!!!!! There is not enough information to answer this. Your supposedly correct solutions is just one of the possible answers. Here is another solution. The first cut is a vertical cut down the middle which makes two equal semi-circles. He then cuts the pizza horizontally, three fourths down the width of the pizza (If the pizza is an inch thick, 1/4 inch from the bottom) all the .way through both halves. That is 4 slices at an angle of 90 degrees. Is this not another correct answer?

Andrew campbell - 4 years, 4 months ago

The question specifies the cuts go through the centre of the pizza.

Zoe Codrington - 2 years, 2 months ago

I don't agree with this answer Your question said that the cut is a right one so each tip is 90 degrees according to your introduction of the question

Izzat Sh - 6 months, 1 week ago

do you have a answer? cause I don't know.

Am Kemplin - 1 month, 2 weeks ago

I don't agree with this.

Shumail Hassan - 4 years, 11 months ago

Adeeba Hasan
Jan 28, 2017

Since the lines intersect, the angles are vertically opposite. So the equation is 2(3x) + 2x = 360 degrees

Linear Pair

3x+x= 180 4x=180 x= 45°

3(45°)= 135°

Kevin Silva - 2 months ago

Lazy Pizza Parlor

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