https://file.aiquickdraw.com/mathbot/file/17267465000611h82rke4.jpg

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 \(360^\circ\).

Find the value of the unknowns in each shape (a trapezoid and a parallelogram).

Learn how to find the unknown angles in a trapezoid and a parallelogram. This problem uses geometric properties like the angle sum property and theorems for opposite and adjacent angles in quadrilaterals. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation