Relationship: Supplementary angles add up to 180^(∘)
B
b x = 5^(∘)
Relationship: Alternate exterior angles are congruent
C
c x = 15^(∘)
Relationship: Triangle Angle Sum Theorem
D
d x = 35^(∘)
Relationship: Exterior angles equal the sum of the remote interior angles
Practice makes perfect
a We have been asked to find the value of x in the given diagram.
Notice that the two smaller angles form a linear pair. This means that their measures must add up to 180^(∘).
(4x-3^(∘)) + (3x+1^(∘)) = 180^(∘)
Let's solve the equation for x.
The diagram shows a triangle with the measures of all of its interior angles expressed in terms of x. By the Triangle Angle Sum Theorem, these measures will add up to 180^(∘).
x+19^(∘) + 4x+28^(∘) + 3x+13^(∘) = 180^(∘)
Let's solve the equation for x.
The Triangle Exterior Angle Theorem tells us that the measure of an exterior angle of a triangle is equal to the sum of its two remote interior angles. This means that for our triangle, the sum of 40^(∘) and 90^(∘) equals 4x-10^(∘).
40^(∘) + 90^(∘) = 4x-10^(∘)
Let's solve our equation for x.
