Question

I NEED HELP WITH THIS ASAP 100 POINTS IF SOMEONE GETS THIS RIGHT.
Question 12(Multiple Choice Worth 2 points)
(Interior and Exterior Angles MC)

For triangle XYZ, m∠X = (4g + 13)° and the exterior angle to ∠X measures (3g + 48)°. Find the measure of ∠X and its exterior angle.

Interior angle = 48°; exterior angle = 74.25°
Interior angle = 74.25°; exterior angle = 48°
Interior angle = 81°; exterior angle = 99°
Interior angle = 99°; exterior angle = 81°

Answer 1

Answer:

Interior angle = 81°; exterior angle = 99°.

Step-by-step explanation:

For triangle XYZ:

• m∠X = (4g + 13)°
• exterior angle to ∠X = (3g + 48)°

Angle X and its exterior angle form a straight line.

Angles on a straight line sum to 180°.

Therefore:

⇒ (4g + 13)° + (3g + 48)° = 180°

⇒ 4g + 13 + 3g + 48 = 180

⇒ 7g + 61 = 180

⇒ 7g + 61 - 61 = 180 - 61

⇒ 7g = 119

⇒ 7g ÷ 7 = 119 ÷ 7

⇒ g = 17

To find the measure of ∠X and its exterior angle, substitute the found value of g into the angle expressions:

⇒ m∠X = (4(17) + 13)°

⇒ m∠X = (68 + 13)°

⇒ m∠X = 81°

⇒ exterior angle to ∠X = (3(17) + 48)°

⇒ exterior angle to ∠X = (51 + 48)°

⇒ exterior angle to ∠X = 99°

Therefore:

• Interior angle = 81°
• Exterior angle = 99°