Question

1. A quadrilateral has three acute angles, each measure 80°. What is the measure of the fourth angle?

2. In a quadrilateral ABCD, the measure of the three angles A, B and C of the quadrilateral is 110°, 70° and 80°, respectively. Find the measure of the fourth angle.

please solve it​

Answer 1

Answer:

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Step-by-step explanation:

1) If the quadrilateral has three acute angles each measuring 80 degrees than the total of the three acute angles will be = 80 x 3 = 240

And since the sum of the 4 angles of the quadrilateral is equal to 360 degrees.

So 240 will be added to the 4th angle =

240 + 4th angle = 360 degrees  

so the 4th angle will be = 360 - 240  

= 120 degrees

So the 4th angle will be 120 degrees.

2)Let,

∠A = 110°

∠B = 70°

∠C = 80°

∠D = x

We know that the sum of all internal angles of quadrilateral ABCD is 360°.

∠A + ∠B+ ∠C+∠D = 360°

110° + 70° + 80° + x = 360°

260° + x = 360°

x = 360° – 260°

x = 100°

Therefore, the fourth angle is 100°.