Question

The sum of two angles of a quadrilateral is 160°. The third angle is equal to the fourth angle. Find their measure.

Answer 1

Answer:

100°

Step-by-step explanation:

As per the provided information in the given question, we have :

• Sum of two angles of a quadrilateral is 160°.
• The third angle is equal to the fourth angle.

We are asked to calculate,

• The measure of the third and the fourth angle.

Let us assume the third and the fourth angle of the quadrilateral as x° each as they both have same measurement.

According to the angle sum property of the quadrilateral, the sum of all the angles of a quadrilateral is equivalent to 360°. Writing it in the form of equation,

$\longmapsto\rm { 1st \; \angle + 2nd \; \angle + 3rd \; \angle + 4th \; \angle = 360^\circ}$

• Here, the sum of two angles of a quadrilateral is 160°.

Substituting the values.

$\longmapsto\rm {160^\circ + 3rd \; \angle + 4th \; \angle = 360^\circ}$

We have assumed the third and the fourth angle as x°, substituting the value.

$\longmapsto\rm {160^\circ + x^\circ + x^\circ= 360^\circ}$

Performing addition in L.H.S.

$\longmapsto\rm {160^\circ + 2x^\circ= 360^\circ}$

Transposing 160° from L.H.S to R.H.S,changing its sign.

$\longmapsto\rm { 2x^\circ= 360^\circ-160^\circ}$

Performing subtraction in R.H.S.

$\longmapsto\rm { 2x^\circ= 200^\circ}$

Transposing 2 from L.H.S to R.H.S. Since, it is in the form of multiplication, it will become in the form of division in R.H.S.

$\longmapsto\rm { x^\circ= \cancel{\dfrac{200^\circ}{2}}}$

Dividing 200 with 2.

$\longmapsto\bf{ x^\circ= 100^\circ}$

Now, we have got the value of x° which is equal to the measure of both third angle and the fourth angle.

$\longmapsto\bf{ 3rd\; angle= 100^\circ}$

$\longmapsto\bf{ 4th\; angle= 100^\circ}$

∴ Measure of the third angle and the fourth angle is 100°.