Question

question 2 find the unknown angles. question 3 find the value of the following pronumerals.

Explanation:

Step1: Recall angle - sum properties

For a triangle, the sum of interior angles is 180°. For a quadrilateral, the sum of interior angles is 360°.

Step2: Solve for Question 2 - a

The figure is a triangle. Let the unknown angle be \(x\). We know that \(x + 30+90 = 180\) (angle - sum property of a triangle). So \(x=180-(30 + 90)=60\).

Step3: Solve for Question 2 - b

The figure is a quadrilateral. Let the unknown angle be \(x\). We know that \(x+90 + 90+100=360\) (angle - sum property of a quadrilateral). So \(x = 360-(90 + 90+100)=80\).

Step4: Solve for Question 3 - a

The figure is a quadrilateral. Let's first find \(z\). Since the adjacent angle to 120° is \(180 - 120=60\) (linear - pair of angles). Then, using the angle - sum property of a quadrilateral \(y+z + 90+125=360\). Since \(z = 60\), we have \(y=360-(60 + 90+125)=85\).

Step5: Solve for Question 3 - b

The figure is a pentagon. The sum of interior angles of a pentagon is \((5 - 2)\times180=540\). Let the unknown angle be \(x\). Then \(x+30+90+120+150 = 540\), so \(x=540-(30 + 90+120+150)=150\).

Step6: Solve for Question 3 - c

The figure is a triangle. Let the unknown angle be \(x\). We know that \(x+90+70 = 180\) (angle - sum property of a triangle), so \(x=180-(90 + 70)=20\).

Step7: Solve for Question 3 - d

The figure is a quadrilateral. Let's first consider the right - angled triangle part. In the right - angled triangle, if one angle is 70°, then the other non - right angle is \(180-(90 + 70)=20\). Let the unknown angles in the quadrilateral be \(x\) and \(y\). We know that \(x + y+90+70=360\). Also, from the right - angled triangle part, we can find the relationships. If we assume the small right - angled triangle, the angle adjacent to \(x\) in the non - right part is 20°. Then \(x = 160\) and \(y = 40\).

Step8: Solve for Question 3 - e

The figure is a parallelogram - like shape. Opposite angles are equal. Let the unknown angles be \(x\) and \(y\). We know that \(x = 130\) (opposite angles are equal) and \(y = 50\) (adjacent angles in a parallelogram - like shape are supplementary, \(180 - 130=50\)).

Step9: Solve for Question 3 - f

The figure is a hexagon. The sum of interior angles of a hexagon is \((6 - 2)\times180 = 720\). Let the unknown angle be \(x\). Then \(x+90+90+120+150+120=720\), so \(x=720-(90 + 90+120+150+120)=150\).

Answer:

Question 2 - a: 60°
Question 2 - b: 80°
Question 3 - a: \(y = 85\), \(z = 60\)
Question 3 - b: 150°
Question 3 - c: 20°
Question 3 - d: \(x = 160\), \(y = 40\)
Question 3 - e: \(x = 130\), \(y = 50\)
Question 3 - f: 150°