Question

Quadrilateral BOAT is an isosceles trapezoid.


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If m T = 130°, find m O.

50°
115°
130°

Answer 1

@peachpi

Answer 2

@geerky42

Answer 3

@TheSmartOne

Answer 4

115?

Answer 5

angle T and A are equal
so add 130+130=260
360-260=?
? DIVIDED BY 2 = ?
BECAUSE ANGLE O AND ANGLE B ARE EQUAL

Answer 6

50?

Answer 7

@happy_to_help

Answer 8

CORRECT

Answer 9

thnx

Answer 10

By definition of an isoceles trapezoid we can conclude that:
\[<T=<A=130\]
\[<B=<O= \beta\]
What I did was using the definition of an isoceles trapezoid to create some ground o work with, because we can't work with a diagram alone, of course.

As a personal tip:
Whenever you face a geometry excercise or proof you always start by relating the hypothesis, wich is the given information.

So, a trapezoid is but a convex cuadrilateral that has two unequal parallel sides, it also has a ery useful propety, it has two pairs of equal angles, and those angles happen to be the superior and the inferior ones.
So, if we call them alpha and beta, they will follow this equation:
\[2 \beta + 2 \alpha =360\]
where 2(beta) is the sum of the inferior angles, wich in perspective is angle "B" and "O" respectively.
And 2(alpha) the sum of the superior angles, wich happen to be angle "T" and angle "A", and this is true for all the isoceles trapezoids.
As a note, all the angles in any quadrilateral sum up to 360 degree.