Question

1. which of the following statements is false?$\bigcirc$ bo = 7.8 cm$\bigcirc$ $c_1$ = 40°$\bigcirc$ ao = 7.8 cm$\bigcirc$ $a_2$ = 40°

Explanation:

Step1: Identify quadrilateral type

The figure is a parallelogram (opposite sides equal, alternate interior angles match: $\angle a_1 = 40^\circ$, $\angle d_1 = \angle b_1$, $\angle a_2 = \angle c_1$, $\angle d_2 = \angle b_2$). In a parallelogram, diagonals bisect each other, so $AO=OC$, $BO=OD$.

Step2: Verify each option

• Option 1: $BO=7.8$ cm. Since $OD=7.8$ cm and diagonals bisect, this is true.
• Option 2: $c_1=40^\circ$. $\angle c_1 = \angle a_1$ (alternate interior angles), so this is true.
• Option 3: $AO=7.8$ cm. $OC=7.8$ cm, and $AO=OC$ (diagonals bisect), so this is true.
• Option 4: $a_2=40^\circ$. $\angle a_2 = \angle c_1$, but $\angle c_1$ is not $40^\circ$ (the $40^\circ$ angle is adjacent to $\angle c_1$; $\angle a_1=40^\circ$, $\angle a_2$ is a different angle in the parallelogram's diagonal split, so this is false).

Answer:

$\boldsymbol{a_2 = 40^\circ}$