Question

If three acute angles of a quadrilateral measure 70° each, then the measure of the fourth angle is___________________.

Answer 1

Hint: Study the property of the quadrilateral. Learn about the measure of the four angles of the quadrilateral. The measure of four angles of a quadrilateral is 360 degrees.
Formula used: The sum of the four angles of a quadrilateral ABCD is, $$\mathrm{\angle }A+\mathrm{\angle }B+\mathrm{\angle }C+\mathrm{\angle }D={360}^{\circ }$$ where, $$\mathrm{\angle }A,\mathrm{\angle }B,\mathrm{\angle }C$$ and $$\mathrm{\angle }D$$ are the four angles of the quadrilateral.

Complete step by step solution:
We have given here a quadrilateral whose three angles are acute angles. Measure of each angle of the quadrilateral is $${70}^{\circ }$$ . We have to find the measure of the fourth angle.
Now, we know that the sum of the four angles of a quadrilateral ABCD is, $$\mathrm{\angle }A+\mathrm{\angle }B+\mathrm{\angle }C+\mathrm{\angle }D={360}^{\circ }$$ where, $$\mathrm{\angle }A,\mathrm{\angle }B,\mathrm{\angle }C$$ and $$\mathrm{\angle }D$$ are the four angles of the quadrilateral.
So, the sum of three angles of the quadrilateral given here is,

 $$\mathrm{\angle }A+\mathrm{\angle }B+\mathrm{\angle }C={70}^{\circ }\times 3={210}^{\circ }$$ [ Let, four angles are $$\mathrm{\angle }A,\mathrm{\angle }B,\mathrm{\angle }C$$ and $$\mathrm{\angle }D$$ respectively]
So, the fourth angle of the quadrilateral is the difference between 360 and the sum of the three angles. $$\mathrm{\angle }D={360}^{\circ }-(\mathrm{\angle }A+\mathrm{\angle }B+\mathrm{\angle }C)$$
Or, $$\mathrm{\angle }D={360}^{\circ }-{210}^{\circ }={150}^{\circ }$$
So, the measure of the fourth angle is $${150}^{\circ }$$
So, the correct answer is “ $${150}^{\circ }$$ ”.

Note: The sum of the three angles of a triangle is $${180}^{\circ }$$ and the sum of the four angles of a quadrilateral is always equal to $${360}^{\circ }$$ . For different types of quadrilaterals with the said property they have additional properties. For example, the sum of opposite angles of a quadrilateral inside a circle is $${180}^{\circ }$$ . Each angle of a square is a right angle. The opposite angle of a parallelogram is equal.