If the decagon has all equal sides, and the measure of angle atb is 120°, find the degree measure of angle tbp. a)48 b)24 c)22 d)18 e)12

Consider the given decagon of all equal sides.

Given:

To find:

Construction: Join a dotted line from point T to P.

Now, and lies on the straight line. Hence, they form linear pair.

Therefore,

(equation 1)

Now, consider triangle TBP with two equal sides TB and BP.

By using the property

"Angles opposite to equal sides of an isosceles triangle are equal."

Since TB=BP, therefore the angles opposite to these sides are also equal.

From equation 1,

Now, in triangle TBP,

By using angle sum property, which states

" The sum of measures of all three angles of a triangle is 180 degrees"

So, the measure of angle TBP is 60 degrees.