Measure of the supplement of angle abc is (18x + 22) degrees. measure of the complement of angle abc is (9x - 5) degrees. determine m to abc

∠ABC = 32°

Step-by-step explanation:

Supplementary angles : A pair of angles whose sum is 180°

We are given that Measure of the supplement of angle ABC is (18x + 22)°

⇒∠ABC +  (18x + 22)° =180°

⇒∠ABC =180° - (18x + 22)°

⇒∠ABC = 180° - 18x - 22°

⇒∠ABC = (158 - 18x)°  --1

Complementary angles : A pair of angles whose sum is 90°

We are given that Measure of the complement of angle ABC is (9x - 5)°

⇒∠ABC +  (9x-5)° =90°

⇒∠ABC =90° - (9x -5)°

⇒∠ABC = 90° - 9x +5°

⇒∠ABC = (95-9x)°  --2

So, equating 1 and 2

⇒(158 - 18x)° = (95-9x)°

⇒158-95 = -9x+18x

⇒63 =9x

⇒

⇒ x = 7

Now to find ∠ABC

Substitute the value of x in equation 1

∠ABC = (158 - 18*7)°

∠ABC = 32°

Hence ∠ABC = 32°

step-by-step explanation:

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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.