Question

4

Jorge is improving the structural stability of a table
by reinforcing the table's leg joints with triangular
cross-braces. The cross-braces will connect the
points where legs are attached to the tabletop to
the midpoint of the bottom of the table's base.
Notice in his sketch that the cross-braces will form
a 53° angle with each other, and will form two
angles that both measure x° with the legs of the
table.
PLEASE HELP WITH THESE QUESTION

Answer 1

x° = 26.5

Explanation:

Each triangle is a right triangle; one angle = 90°, second angle = x° , and the third angle = 63.5° because the 53° + the two angles adjacent to 53° is will = 180° which is the measure of a straight angle and those two angles are equal because the triangles are congruent by HA ; 180° - 53° = 127° ÷ 2 = 63.5°.

Now each triangle angles = 180° so 90° + x° + 63.5° = 180°; 153.5° + x° = 180;

x° = 180 - 153.5; x° =26.5°