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Lesson Example Discussion Quiz: Class Homework

Example

Title: Angles

Grade: 1400-a Lesson: S3-L8

Explanation: Hello Students, time to learn examples. Let us take turns and read each example. Explain each step. Pay special attention to steps and pictures and communicate in your own words.

Examples:

In a quadrilateral, two consecutive angles are acute, and their measures are in the ratio 3:5. If the smaller angle measures 45 degrees, find the measure of the larger acute angle.

Step 1a

n a quadrilateral, the sum of all angles is 360 degrees.

Let’s call the two consecutive acute angles x and y.

We know that x : y = 3 : 5. We also know that x = 45 degrees.

Explanation: Let’s denote the measures of the two consecutive acute angles as 3x and 5x, where x is a common factor representing the ratio.
Given that the smaller angle measures 45 degrees, we have: x = 45

Step 2a

Now we find out the y value

y = \$5/3\$

x = \$(5/3) \times 45\$ degrees

Explanation: Now, we can find the value of x: x = \$45 / 3\$

x = \$15\$

Step 3a

After Simplification

y = \$5 \times 15 = 45\$ degrees

Explanation: Now that we have the value of x, we can find the measure of the larger acute angle: 5x

⇒ \$5\times15\$

⇒ \$75\$ degrees

Step 4a

Therefore, the measure of the larger acute angle is 75 degrees.

Explanation: So, the measure of the larger acute angle in the quadrilateral is 75 degrees.