Question

Help plz ASAP and explain the answer

Answer 1

Given:

It is given that the measurements of the triangle.

The measure of ∠2 is (3x + 3)°

The measure of ∠3 is (3x - 4)°

The measure of ∠4 is (5x + 8)°

We need to determine the measure of ∠1 and ∠4.

Value of x:

The value of x can be determined using the exterior angle theorem.

Applying the theorem, we have;

$m \angle 4=m \angle 2+m \angle 3$

Substituting the values, we get;

$5x+8=3x+3+3x-4$

$5x+8=6x-1$

$-x+8=-1$

     $-x=-9$

        $x=9$

Thus, the value of x is 9.

Measure of ∠4:

Substituting the value of x in the expression of ∠4, we get;

$m\angle 4=5(9)+8$

       $=45+8$

$m\angle 4=53^{\circ}$

Thus, the measure of ∠4 is 53°

Measure of ∠1:

The angles 1 and 4 are linear pairs and hence these angles add up to 180°

Thus, we have;

$\angle 1+ \angle 4=180^{\circ}$

Substituting the values, we get;

$\angle 1+ 53^{\circ}=180^{\circ}$

         $\angle 1=127^{\circ}$

Thus, the measure of ∠1 is 127°