In the given image, we have two shapes (a) and (b), and we are tasked with finding the unknown angles. Let’s break down each shape:

(a) Trapezoid

• The figure has two given angles: $98^\circ$ and $47^\circ$.
• We need to find $a$ and $b$.

Solution:

1. Opposite angles of a trapezoid: In a trapezoid, the sum of adjacent angles along the same side is $180^\circ$ (since they are supplementary).

   • For $a$ and $98^\circ$: $a + 98^\circ = 180^\circ \implies a = 180^\circ - 98^\circ = 82^\circ$

   • For $b$ and $47^\circ$: $b + 47^\circ = 180^\circ \implies b = 180^\circ - 47^\circ = 133^\circ$

   Thus, $a = 82^\circ$ and $b = 133^\circ$.

(b) Parallelogram

• The figure has one given angle: $58^\circ$.
• We need to find $c$, $d$, and $e$.

Solution:

1. Opposite angles of a parallelogram: In a parallelogram, opposite angles are equal, and adjacent angles are supplementary (sum to $180^\circ$).

   • For $e$: Since $e$ is opposite $58^\circ$, we have: $e = 58^\circ$

   • For $c$ and $d$: These are adjacent angles to $58^\circ$, so they must sum to $180^\circ$: $c + 58^\circ = 180^\circ \implies c = 180^\circ - 58^\circ = 122^\circ$ Similarly, $d$ is opposite $c$, so: $d = 122^\circ$

   Thus, $e = 58^\circ$, $c = 122^\circ$, and $d = 122^\circ$.

Summary:

• (a): $a = 82^\circ$, $b = 133^\circ$
• (b): $c = 122^\circ$, $d = 122^\circ$, $e = 58^\circ$

Would you like further details on any of these steps?

Here are some related questions for further practice:

1. What is the sum of the interior angles of a trapezoid?
2. How do you prove that opposite angles in a parallelogram are equal?
3. Can a parallelogram have all angles equal? If so, what type of shape is it?
4. What are the properties of adjacent angles in a cyclic quadrilateral?
5. How do you calculate the angles in an isosceles trapezoid?

Tip: In any quadrilateral, the sum of the interior angles is always $360^\circ$.