Focus on different triangles to find the measures of each angle.
m∠ 1=55^(∘)
m∠ 2=75^(∘)
m∠ 3=55^(∘)
m∠ 4=15^(∘)
Practice makes perfect
We are asked to find the measure of four angles, but we do not have to do it in the order of the numbering.
We will find the measures in the following order.
m∠ 1,m∠ 3,m∠ 4,m∠ 2
Finding m∠ 1
Notice that ∠ 1 is one of the acute angles of a right triangle. Notice also that the measure of the other acute angle of this right triangle is given on the figure.
Notice that ∠ 3 and an angle with a measure of 35^(∘) together form a right angle.
If two adjacent angles form a right angle, then their measure add to 90^(∘). Since we know the measure of one of these angles, this lets us find the measure of the other.
Let's put the measure of ∠ 3 we just found on the diagram and focus on the triangle with ∠ 3 and ∠ 4 as interior angles.
Notice that the measure of an exterior angle for this triangle is given on the figure.
The Exterior Angle Theorem tells a relationship between these angles.
The measure of the exterior angle
is the sum of the measures
of the two remote interior angles.
This lets us set up and solve an equation for m∠ 4.
