Question

Two congruent, isosceles triangles are joined to form a parallelogram. The largest angle of the parallelogram is 116°. Write two equations and solve them to find out the value of 'a' and 'b'.

A) a + b = 180°, 2a + 2b = 360°
B) a + b = 90°, 2a + 2b = 180°
C) a + b = 116°, 2a + 2b = 232°
D) a + b = 45°, 2a + 2b = 90°

Answer 1

To find the values of 'a' and 'b', set up the equations a + b = 180° and 2a + 2b = 360°. Solving these equations gives a = 116° and b = 64°.

Step-by-step explanation:

To find the values of 'a' and 'b', we can use the fact that the largest angle of the parallelogram is 116°. Since the angles of a parallelogram add up to 360°, we can set up the equation 2a + 2b = 360°. Additionally, since the two congruent, isosceles triangles form a parallelogram, the angles opposite the congruent sides are equal. This means that a + b = 180°. Solving these two equations, we get a = 116° and b = 64°.