Question

13. The diagonals of a rhombus ABCD intersect at O. Given that measure of angle BAC is 75°,
find the measure of angle ABO.

Answer 1

Answer:

Let ABCD be the given parallelogram and ∠A be the given angle.

∴∠A=68°

As we know that, in a parallelogram opposite angles are equal.

∴∠C=∠A=68°

Let the measurement of ∠B be x°.

∴∠D=∠B=x°(∵Opposite angles)

Now as we know that sum of all the angles in a parallelogram is 360°.

∴68°+x°+68°+x°=360°

⇒2x°+136°=360°

⇒2x°=360°−136°

⇒x°=

2

224°

=112°