SOLUTION: Quadrilateral MATH is a kite. Find the measure of angle A , at the top of the kite it says M = 135* and the T at the bottom says 53*

Question 830235: Quadrilateral MATH is a kite. Find the measure of angle A , at the top of the kite it says M = 135* and the T at the bottom says 53*
Found 3 solutions by Edwin McCravy, AnlytcPhil, KMST:
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!

given: kite MATH, m∠M=135�, m∠T=53� to find: m∠MAT (same as ∠M before we drew the green diagonal below) m(MA) = m(MH) ΔMAH is isosceles m∠MAH = m∠MHA m∠M+m∠MAH+m∠MHA = 180� m∠M = 135� 135�+m∠MAH+m∠MHA = 180� m∠MAH+m∠MHA = 180�-135� m∠MAH+m∠MAH = 45� 2m∠MAH = 45� m∠MHA = 22.5� -------------- m(TA) = m(TH) ΔTA is isosceles m∠TAH = m∠THA m∠T+m∠TAH+m∠THA = 180� m∠T = 53� 53�+m∠TAH+m∠THA = 180� m∠TAH+m∠THA = 180�-53� m∠TAH+m∠TAH = 127� 2m∠TAH = 127� m∠TAH = 63.5� ---------------------------- ∠MAT = m∠MAH+m∠TAH = 22.5�+63.5� = 86� Edwin

Answer by AnlytcPhil(1806)   (Show Source): You can put this solution on YOUR website!

given: kite MATH, m∠M=135�, m∠T=53� to find: m∠MAT (same as ∠M before we drew the green diagonal below) m(MA) = m(MH) ΔMAH is isosceles m∠MAH = m∠MHA m∠M+m∠MAH+m∠MHA = 180� m∠M = 135� 135�+m∠MAH+m∠MHA = 180� m∠MAH+m∠MHA = 180�-135� m∠MAH+m∠MAH = 45� 2m∠MAH = 45� m∠MHA = 22.5� -------------- m(TA) = m(TH) ΔTA is isosceles m∠TAH = m∠THA m∠T+m∠TAH+m∠THA = 180� m∠T = 53� 53�+m∠TAH+m∠THA = 180� m∠TAH+m∠THA = 180�-53� m∠TAH+m∠TAH = 127� 2m∠TAH = 127� m∠TAH = 63.5� ---------------------------- ∠MAT = m∠MAH+m∠TAH = 22.5�+63.5� = 86� Edwin

Answer by KMST(5328)   (Show Source): You can put this solution on YOUR website!
ANOTHER WAY TO THE SOLUTION:
The sum of the measures of the interior angles in a polygon with sides is .
In particular, the sum of the measures of the interior angles in a quadrilateral is .
The angles at A, and H are congruent (they have the same measure), because a kite is symmetrical, so if is the measure of those angles,

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