Question

Two adjacent angles of a parallelogram are in the ratio 4 : 5 Find their measures​

Answer 1

Question

Two adjacent angles of a parallelogram are in the ratio 4 : 5. Find their measures

Solution

Given that the two adjacent angles of a parallelogram are in the ratio 4 : 5. Now let's Assume these adjacent angles be ∠A and ∠B whose measures are 4x and 5x respectively.

We know that :

Sum of adjacent angles of Parallelogram = 180°

∠A + ∠B = 180°

↦ 4x + 5x = 180°

↦ 9x = 180°

↦ x = 180/9 = 20°

Therefore, we get the measure of two adjacent angles i.e∠A = 4x = 4 × 20 = 80°

∠B = 5x = 5 × 20 = 100°

Here, after attaining two adjacent angles we can even proceed solving for third and fourth adjacent angles :

∠B + ∠C = 180° (sum of adjacent angles)

↦ 100° + ∠C = 180°

↦∠C = 180° - 100° = 80°

Also, ∠C + ∠D = 180°

↦ 80° + ∠D = 180°

↦ ∠D = 180° - 80° = 100°

Measures of all four angles of parallelogram are 80°, 100°, 80° & 100°.

$\underline{\rule{190pt}{2pt}}$

Thankyou

Answer 2

Solution

We know that :

Sum of adjacent angles of Parallelogram = 180°

∠A + ∠B = 180°

↦ 4x + 5x = 180°

↦ 9x = 180°

↦ x = 180/9 = 20°

• ∠A = 4x = 4 × 20 = 80°

• ∠B = 5x = 5 × 20 = 100°

∠B + ∠C = 180° (sum of adjacent angles)

↦ 100° + ∠C = 180°

↦∠C = 180° - 100° = 80°

Also, ∠C + ∠D = 180°

↦ 80° + ∠D = 180°

↦ ∠D = 180° - 80° = 100°

Measures are 80°, 100°, 80° & 100°.