The ratio of the angle measures of a triangle is 1:2:2. What is the value of the smallest angle?
36°
90°
180°
72°
The three angles are x, 2x, 2x
So,
x+2x+2x = 180
x = 36
To find the value of the smallest angle in a triangle when the angle measures are given in a ratio, you need to divide the total angle measure by the sum of the ratio parts and then multiply by the corresponding ratio part.
In this case, the ratio of the angle measures is 1:2:2, which means the total ratio parts is 1 + 2 + 2 = 5.
To find the value of the smallest angle:
1. Divide the total angle measure (180° for a triangle) by 5: 180° / 5 = 36°.
2. Multiply the smallest ratio part (1) by the result from step 1: 36° * 1 = 36°.
Therefore, the value of the smallest angle is 36°.
To find the value of the smallest angle in a triangle with a ratio of 1:2:2 for the angle measures, we need to remember that the sum of all the angles in a triangle is always 180°.
Step 1: Add up the ratio values.
The total ratio values are 1 + 2 + 2 = 5.
Step 2: Calculate the size of each angle.
To find the size of each angle, we divide the total angle measure (180°) by the total ratio values (5).
The smallest angle = (1 / 5) × 180°
The second angle = (2 / 5) × 180°
The largest angle = (2 / 5) × 180°
Step 3: Calculate the smallest angle.
Now we can find the value of the smallest angle.
The smallest angle = (1 / 5) × 180° = 36°
Therefore, the value of the smallest angle is 36°.