Q13. - Geometry

Question

a. Draw a three large circles and inscribe a different shaped quadrilateral $ABCD$ in each.

    b. Use a protractor to measure all the angles.

    c. Compute $m\angle A+m\angle C$ and $m\angle B+m\angle D.$.

    d. What is the relationship between opposite angles of an inscribed quadrilateral?

Step-by-Step Solution

Answer

(a)

The final answer  is

(b)

The final answer  is

(c)

The final answer  is

$\angle A+\angle C=180 \text{and}\angle B+\angle D=180$

a. Step 1. Given information:

The quadrilateral ABCD.

Angles= $m\angle A,m\angle B,m\angle C,m\angle D.$

Step 2. Concept used:

We use basic geometric and angle concept

Step 3. Applying the concept:

The above figure is the required figure that can be drawn from the given information.

b. Step 1. Given information:

The quadrilateral ABCD.

Angles= $m\angle A,m\angle B,m\angle C,m\angle D.$

Step 2. Concept used:

 We use basic geometric and angle concept

Step 3. Applying the concept:

c. Step 1. Given information:

The quadrilateral ABCD.

Angles= $m\angle A,m\angle B,m\angle C,m\angle D.$

Step 2. Concept used:

We use basic geometric and angle concept

Step 3. Applying the concept:

A circle with inscribe quadrilateral is drawn below.

Here, opposite angles are supplementary which means.

$\begin{array}{l}\angle A+\angle C={180}^{\circ }\\ \angle B+\angle D={180}^{\circ }\end{array}$