Question

Can anyone help me please ASAP

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°