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Lesson Example Discussion Quiz: Class Homework

Step-1

Title: Angles

Grade: 10-a Lesson: S1-L2

Explanation:

Step	Type	Explanation	Answer
1	Problem	In a triangle, one angle is an obtuse angle, and the other two angles are in a ratio of 3:4. The sum of the measures of the two acute angles is 100 degrees. Find the measure of the obtuse angle.
2	Step	Given	Let’s denote the measures of the two acute angles as 3x and 4x, where x is a common factor and the sum of the measures of the two acute angles is 100 degrees.
3	Step	Two acute angles	3x + 4x = 100
4	Step	After simplication we get	7x = 100
5	Step	After simplication we get	x = 14.285
6	Step	Now substitute the x value	3x = \$3 times 14.285\$ = 42.855 degrees
7	Step	Now substitute the x value	4x = \$4 times 14.285\$ = 57.128 degrees
8	Step	sum of the measures of all three angles in a triangle is always 180 degrees	Obtuse angle = 180 - (42.855 + 57.128) ≈ 80.017 degrees
9		Answer	Obtuse angle = 80.017 degrees

Step

Type

Explanation

Answer

Problem

In a triangle, one angle is an obtuse angle, and the other two angles are in a ratio of 3:4. The sum of the measures of the two acute angles is 100 degrees. Find the measure of the obtuse angle.

Step

Given

Let’s denote the measures of the two acute angles as 3x and 4x, where x is a common factor and the sum of the measures of the two acute angles is 100 degrees.

Step

Two acute angles

3x + 4x = 100

Step

After simplication we get

7x = 100

Step

After simplication we get

x = 14.285

Step

Now substitute the x value

3x = \$3 times 14.285\$ = 42.855 degrees

Step

Now substitute the x value

4x = \$4 times 14.285\$ = 57.128 degrees

Step

sum of the measures of all three angles in a triangle is always 180 degrees

Obtuse angle = 180 - (42.855 + 57.128) ≈ 80.017 degrees

Answer

Obtuse angle = 80.017 degrees