Two adjacent angles of a parallelogram are in the ratio 4 is to 5

Two adjacent angles of a parallelogram are in the ratio 4:5. Find the measure of measure of each of its angles. What does ratio 4:5 mean? How do we set up the problem to solve for the angles?

Method 1:

Both methods should provide same results.

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Ex 3.4, 1 State whether True or False. (a) All rectangles are squares A rectangle is a parallelogram where one angle is 90° A square is a parallelogram where all angles are 90° and all sides are equal Since, rectangle has only Opposite sides equal whereas a square has all the sides equal. ∴ All rectangles are not squares. ⇒ Statement is False

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Two adjacent angles of a parallelogram are in the ratio 4 : 5. Find the measure of each of its angles.

Solution

The ratio between two adjacent angles of a || gm ABCD are in the ratio 4 : 5

Let $\angle A=4xand\angle B=5x$

But $\angle A+\angle B={180}^{\circ }$

$\Rightarrow 4x+5x={180}^{\circ }$

$\Rightarrow 9x={180}^{\circ }$

$\therefore x=\frac{{180}^{\circ }}{9}={20}^{\circ }$

$\therefore \angle A=4x=4\times {20}^{\circ }={80}^{\circ }$

$\angle B=5x=5\times 20={100}^{\circ }$

Mathematics

Secondary School Mathematics VIII

Standard VIII