An angle measures 40.2° more than the measure of its complementary angle. What is the measure of each angle?

and

Recall that Angles that are complementary to each other add up to .

Let be the measure of the complementary angle.

If an angle is more than its complementary angle, the measure of that angle is . The sum of both angles are expressed but since the have to add to as they are complementary, .

Solving for :

Since the other angle measures , we can plug in the value of to find the measure of the angle.

Evaluating :

The measure of the angles are and

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.