Question

the measure of one angle of a right triangle is 30° more than the measure of the smallest angle. find the measures of both acute angles.
smaller angle =
larger angle =
question help: written example message instructor
submit question
question 8
the triangles are similar. find the value for x, and include the correct units.
figure is not drawn to scale.
x =
question help: video message instructor
submit question

Explanation:

First Problem (Right Triangle Angles)

Step1: Define variables for angles

Let $x$ = smaller acute angle, $x+30^\circ$ = larger acute angle.

Step2: Sum of acute angles is $90^\circ$

$x + (x + 30^\circ) = 90^\circ$

Step3: Simplify and solve for $x$

$2x + 30^\circ = 90^\circ$
$2x = 90^\circ - 30^\circ = 60^\circ$
$x = \frac{60^\circ}{2} = 30^\circ$

Step4: Find larger angle

$x + 30^\circ = 30^\circ + 30^\circ = 60^\circ$

Step1: Set up proportion for similar triangles

Corresponding sides are proportional: $\frac{22}{x} = \frac{18}{45}$

Step2: Cross-multiply to solve for $x$

$18x = 22 \times 45$
$18x = 990$
$x = \frac{990}{18} = 55$

Answer:

Smaller angle = $30^\circ$
Larger angle = $60^\circ$

---

Second Problem (Similar Triangles)