Question

Find measures of all the four angles of a quadrilateral if two of them are twice of the third and fourth is 20 degree more than the sum of two equal angles

Answer 1

Answer:

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Answer 2

$x=y=75.6^{\circ}$

$z=37.8^{\circ}$

$w=171.2^{\circ}$

Step-by-step explanation:

Let x, y,z and w are four angles of quadrilateral.

According to question

$x=2z,y=2z$

$w=(x+y)+20=2z+2z+20=4z+20$

$x+y+z+w=360^{\circ}$

By the property of sum of angles of quadrilateral.

Substitute the values

$2z+2z+z+4z+20=360$

$9z=360-20=340$

$z=\frac{340}{9}=37.8^{\circ}$

$z=37.8^{\circ}$

$x=y=2\times 37.8=75.6^{\circ}$

$w=4(37.8)+20=171.2^{\circ}$

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