Explanation

The angle sum of a triangle will always be equal to 180°.

The angle sum of a quadrilateral is equal to 360°

And a triangle can be created by slicing a quadrilateral in half from corner to corner. Since a triangle is essentially half of a quadrilateral

Its angle measures should be half as well. Half of 360° is 180°

Explanation

Acute angles measure less than 90 degrees.

Right angles measure 90 degrees.

Obtuse angles measure more than 90 degrees.

agm.04.03.23

Explanation

2x+3=3x−2

First, let's move all terms involving x to one side of the equation. We can do this by subtracting 2x from both sides:

2x+3−2x=3x−2−2x

3=x−2

Next, let's isolate x by adding 2 to both sides:

3+2=x−2+2

5=x

So, the solution to the equation is x=5.

Explanation

To find the range from a set of data, subtract the smallest value from the largest value.

Given data:

85, 87, 90, 92, 95

Smallest value: 85

Largest value: 95

Range=Largest value−Smallest value

Range=95−85

Range=10

So, the range of the data set is 10.

Explanation

To find the cost of one pen, divide the total cost by the number of pens:

Cost of one pen = Total cost /Number of pens

Given:

Total cost for 5 pens = 125 rupees

Number of pens = 5

Cost of one pen= 125rupees / 5

Cost of one pen=25rupees

So, the cost of one pen is 25 rupees.

Explanation

Plane geometry has two dimensions

It deals with shapes like lines, circles, and polygons that exist on a flat plane.

Explanation

Let the three consecutive integers be  x+1, and  x+2.

According to the problem, their sum is 72:

x+(x+1)+(x+2)=72

Combine like terms: 

3x+3=72

Subtract 3 from both sides: 

3x=69

Divide by 3: 

x=23

Explanation

To find the volume of a rectangular box, we use the formula:

Volume=Length×Width×Height

Given the dimensions of the box:

Length (𝐿) = 10 cm

Width (𝑊) = 15 cm

Height (𝐻) = 20 cm

Plug these values into the formula:

Volume=10cm×15cm×20cm

Volume=10×15×20

Volume=150×20

Volume = 3000cm^3

So, the volume of the rectangular box is 3000cm^3

 .

Explanation

Number of pizzas = 4 pizzas

The number of slices in each pizza = 8 slices

Total number of slices =  slices

4 x 8 = 32 slices

Next, we need to divide the total number of slices by the number of people to find out how many slices each person will get:

Number of people = 6 persons

Number of slices per person = Total number of slices / Number of people

Number of slices per person = 32/6 = 5 slices

Explanation

To find the number of toys sold per day, divide the total number of toys by the number of days:

Toys sold per day = 48 toys/4-day 

=12 toys per day