The sum of the measures of the two remote angles, 35^(∘) and 75^(∘), will give us the measure of the missing angle m∠ 1.
x= 35^(∘) + 75^(∘) ⇒ x = 110^(∘)
b Like in Part A, we want to find the value of x in the given triangle. First, let's look at the given diagram.
The diagram shows an isosceles triangle with one base angle measuring x. By the Base Angles Theorem, the other base angle must also measure x. Let's show this on a diagram.
We want to find the missing angle in the given triangle. Let's use the Triangle Exterior Angle Theorem again.
Now let's apply this theorem to the given triangle.
The sum of the measures of the two remote angles x and x will add up to the measure of the exterior angle 140^(∘).
140^(∘) = x + x ⇒ x = 70^(∘)
c We can use the triangle exterior angle theorem to find the missing measure of our triangle.
Let's apply this theorem to the given triangle.
The sum of the measures of the two remote angles, x^(∘) and 100^(∘), will give us the measure of the exterior angle 148^(∘).
148^(∘)= x^(∘) + 100^(∘) ⇒ x = 48^(∘)
d Let's take a look at the final triangle.
Notice that two of the three angles in the triangle are congruent. Let's call the measure of those angles y. By the Triangle Interior Angles Theorem, the sum of measures of interior angles in a triangle is 180^(∘). Let's write this as an equation for our triangle.
36^(∘) + 2y = 180^(∘)
Now let's solve the equation above for y.
Notice that the angles measuring x and 72^(∘) form a linear pair. This means that their measures must add up to 180^(∘). Let's write this as an equation and solve for x.
x + 72^(∘) = 180^(∘)
⇒
x = 108^(∘)
