Mathematics, 22.01.2022 02:00 nicky123415

The two interior opposite angles of an exterior angle of a triangle are 75° and 85°. Find the measure of the exterior angle

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Answer from: CesarCarvajal969

Exterior angle = m∠160°

Step-by-step explanation:

Given the measures of two interior opposite angles, m75° and m∠85°, and that the prompt requires us to find the measure of the exterior angle of a triangle:

Exterior Angle Theorem

In order to find the measure of the exterior angle, we must apply the Exterior Angle Theorem which states that the measure of an exterior angle of a triangle is equal to the sum of the measures of two non-adjacent remote interior angles.

Solution:

Let x = exterior angle of a triangle

In order to solve for the measure of x, we can set up the following equation:

x = m∠75° + m∠85°

x = 160° ⇒ Measure of the exterior angle of a triangle.

Double-check:

We must verify whether we have the correct value for the exterior angle of a triangle. In reference to the Triangle Sum Theorem, which states that the sum of all interior angles of a triangle is equal to 180°.

Since we already have the measures of the two remote interior angles and the exterior angle of a triangle, we can find the measure of the third interior angle of a triangle by setting up the following equation:

m∠75° + m∠85° + m∠y° = 180°

Where ∠y is the unknown third interior angle of a triangle.

Solve for ∠y (Unknown third interior angle of a triangle)

m∠75° + m∠85° + m∠y° = 180°

160° + m∠y° = 180°

Subtract 160° from both sides of the equation:

160° - 160° + m∠y° = 180° - 160°

m∠y° = 20° ⇒ Third interior angle of a triangle.

Hence, the measures of the three interior angles of a triangle are: 75°, 85°, and 20°, for which the third angle (∠y) and the exterior angle of a triangle (∠x) are supplements:

m∠x° + m∠y° = 180°

160° + 20° = 180°

180° = 180° (True statement).

Therefore, the measure of the exterior angle of a triangle is 160°.

Answer from: Quest

step-by-step explanation:

Answer from: Quest

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is

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The two interior opposite angles of an exterior angle of a triangle are 75° and 85°. Find the measur...

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