M∠cbd=4x+52∘

m∠abc=8x−10∘\qquad m \angle abc = 8x - 10^\circm∠abc=8x−10∘

find m∠cbdm\angle cbdm∠cbd:

 The value of ∠CBD is 98°.

Step-by-step explanation:

Since we have given that

m∠CBD=4x+52∘

and

m∠ABC=8x−10∘

As we know that they are linear pairs.

As we know that a linear pair is a pair of adjacent angles when two lines get intersected by a line say BC.

So, Sum of linear pair is supplementary.

So, m∠CBD = 4x+52=4(11.5)+52=98°

Hence, the value of ∠CBD is 98°.

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.