Solve for m∠.? Please Help!

Question

asked May 15, 2022 167k views

2 Answers

Korpel · Answer 1 · 2022-05-18T13:38:58+0000

Answer:

$\purple {\bold {m\angle A =70\degree}}$

Explanation:

ABCD is a trapezoid. AB || DC and AD is transversal...(given)

$AD \cong BC.. (given)$

Therefore, ABCD is an isosceles trapezoid.

Measures of base angles of isosceles trapezoid are equal.

$\therefore m\angle D =m\angle C$

$\because m\angle C =110\degree... (given)$

$\therefore m\angle D =110\degree$

$m\angle A+ m\angle D =180\degree$

(interior angles on the same side of transversal)

$m\angle A+ 110\degree =180\degree$

$m\angle A =180\degree -110\degree$

$\purple {\bold {m\angle A =70\degree}}$