Question

The measure of the second angle of a triangle is seven more than twice the measure of the first. the third angle is fifteen less than the first. find the meausres of all of the angles. a. 47⁰,101⁰,32⁰ b. 30⁰,80⁰,70⁰ c. 60⁰,50⁰,70⁰ d. 45⁰,90⁰,45⁰

Answer 1

The measure of the first angle is 47 degrees, the second angle is approximately 101 degrees, and the third angle is 32 degrees.

Step-by-step explanation:

We can solve this problem by setting up equations based on the given information.

Let x be the measure of the first angle.

The measure of the second angle is 7 more than twice the measure of the first, so it can be represented as 2x + 7.

The measure of the third angle is 15 less than the first, so it can be represented as x - 15.

The sum of the angles in a triangle is 180 degrees, so we can set up the following equation:

x + (2x + 7) + (x - 15) = 180

Simplifying the equation:

4x - 8 = 180

4x = 188

x ≈ 47

The measures of the angles are approximately: 47°, 2(47) + 7 ≈ 101°, and 47 - 15 = 32°