Question

The measure of two angles of a quadrilateral are 105 degree and 45 degree and the other two angles are equal. Find the measure of each of the equal angles.

Answer 1

Given:

The measure of two angles of a quadrilateral is 105° and 45°

The other two angles are equal

To find:

The measure of each of the equal angles.

Solution:

Let's assume,

∠A = 105°

∠B = 45°

∠C = ∠D = "x" → represent each of the other two equal angles of the quadrilateral.

We know that ⇒ the sum of all 4 angles of the quadrilateral is 360°

i.e., ∠A + ∠B + ∠C + ∠D = 360°

Now, substituting the value of ∠A, ∠B, ∠C & ∠D, we get

$105\° + 45\° + x + x = 360\°$

$\implies 105\° + 45\° + 2x\° = 360\°$

$\implies 150\° + 2x\° = 360\°$

$\implies 2x\° = 360\° - 150\°$

$\implies 2x\° = 210\°$

$\implies x\° = \frac{210\°}{2}$

$\implies \bold{x\° = 105\°}$

Thus, the measure of each of the equal angles is 105°.

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