Find the obtuse angle between the following pair of straight lines.

Given:

To find:

The obtuse angle between the given pair of straight lines.

Solution:

The slope intercept form of a line is

    ...(i)

where, m is slope and b is y-intercept.

The given equations are

On comparing these equations with (i), we get

Angle between two lines whose slopes are is

Putting and , we get

Now,

and

and

and

, so it is an obtuse angle and , so it is an acute angle.

Therefore, the obtuse angle between the given pair of straight lines is 120°.

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.