Referred to the triangle below what is the volume X. 44° (2x + 1) 98°

Solution:

Let us first define the exterior angle theorem of triangles.

Exterior angle theorem:

The measure of the exterior angle is equal to the sum of the measures of the two opposite interior angles.

In the given triangle,

Measure of exterior angle = 98°

Measure of one opposite interior angle = 44°

Measure of other opposite interior angle = (2x + 1)°

To find the value of x:

Using exterior angle theorem,

⇒ 44° + (2x + 1)° = 98°

⇒ 44° + 2x° + 1° = 98°

⇒ 45° + 2x° = 98°

⇒ 2x° = 98° – 45°

⇒ 2x° = 53°

Hence the value of x is .

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is