Question

RRS-1

Answer 1

The missing measures are listed below:

1. $m \angle 1 = m \angle 3 = m \angle 6 = 59^{\circ}$
2. $m\angle 2 = m\angle 4 = m\angle 5 = m \angle 11 = 31^{\circ}$
3. $m\angle 7 = m\angle 8 = m\angle 9 = m\angle 10 = 118^{\circ}$

Procedure - Finding missing angles in a quadrilateral

In this question we must determine the measures of the missing angles by both geometric and algebraic means, whose procedure is presented below:

1. $x = 59^{\circ}$ Given
2. $m \angle 3 = 59^{\circ}$ Alternate internal angles
3. $m \angle 11 = 31^{\circ}$ Complementary angles
4. $m \angle 4 = 31^{\circ}$ Alternate internal angles
5. $m \angle 6 = 59^{\circ}$ Isosceles triangle
6. $m \angle 9 = 62^{\circ}$ Sum of internal angles in a triangle
7. $m \angle 10 = 118^{\circ}$ Supplementary angles
8. $m \angle 8 = 62^{\circ}$, $m\angle 7 = 118^{\circ}$ Vertical angles
9. $m \angle 2 = 31^{\circ}$ Sum of internal angles in a triangle
10. $m \angle 5 = 31^{\circ}$ Sum of internal angles in a triangle
11. $m \angle 1 = 59^{\circ}$ Sum of internal angles in a triangle/Result

The missing measures are listed below:

1. $m \angle 1 = m \angle 3 = m \angle 6 = 59^{\circ}$
2. $m\angle 2 = m\angle 4 = m\angle 5 = m \angle 11 = 31^{\circ}$
3. $m\angle 7 = m\angle 8 = m\angle 9 = m\angle 10 = 118^{\circ}$

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