We want to draw a triangle with angle measures of

4 5^{\circ},

4 5^{\circ},

and

9 0^{\circ} .

We can recall that a triangle can be formed when the sum of the angle measures is equal to

18 0^{\circ} .

Let's check whether the three angle measures add up to

18 0^{\circ} .

4 5^{\circ} + 4 5^{\circ} + 9 0^{\circ} = 18 0^{\circ} ✓

The sum of the angle measures is

18 0^{\circ} .

Now we can construct our triangle. We can begin by drawing an angle of

4 5^{\circ}

using a protractor. Let's call the vertex of this angle

A .

The angle of 45 degrees with its vertex in point A measured by a protractor.

Now we can draw a point $B$ on one of the sides of the angle. Next, we can draw a $4 5^{\circ}$ angle with its vertex at point $B .$

The third vertex of our triangle is the point of intersection between the two rays. We can denote the last vertex as point $C .$ Finally, we can use the protractor to confirm that the measure of the remaining angle is $9 0^{\circ} .$ We can do so in two steps.

Place the center line of the protractor on top of $\overline{B C} .$
Measure the angle between $\overline{B C}$ and $\overline{A C} .$

Let's do it!

The angle formed at $C$ has a measure of $9 0^{\circ} .$ In this case, we can draw a triangle with the given measures.

triangle with angles 45, 45, and 90 degrees

Exercise