Question

The measures of two adjacent angles of a quadrilateral are 52° and 110°. The remaining two adjacent anglas are equal. Find the measure of each of these equal angles.

Answer 1

As we know the sum of all angles is 360°.
Given, two adjacent angles are equal.
Let the angles be X
52+110+X+X=360°
162+2x=360
2x=360-162
X=198÷2
X=99°
So, the two adjacent angles are 99,99°

Answer 2

Answer:

The required measure of each of these equal angles $99^{0}$.

Step-by-step explanation:

Concept used:

A perfect four-sided polygon is referred to as a quadrilateral. In addition, this indicates that a quadrilateral has precisely four vertices and four angles.

The sum of all the angles of a quadrilateral is $360^{0}$

Given:

Two adjacent angles of a quadrilateral are $52^{0}$ ,$110^{0}$

And the remaining two adjacent angles are equal.

To find:

The objective is to find out the measure of each of these equal angles.

Solution:

The sum of the four angles of a quadrilateral is $360^{o}$

Let each of the equal angles is $x^{o}$

$(52+110+x+x)^{o} =360^{o}$

⇒$(162+2x)^{o} =360^{o}$

⇒$2x^{o} =(360-162)^{o}$

⇒$x^{o} =\frac{198^{o} }{2}$

⇒$x^{0} =99^{0}$

Therefore, the measure of each of these equal angles is $99^{0}$.

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