I need helpp pleaseee!! Find the measure of Angle B

Question

asked Aug 19, 2023 54.2k views

2 Answers

Sjh · Answer 1 · 2023-08-23T02:57:06+0000

Answer:

∠B = 78°

Explanation:

The sum of the measures of the interior angles of a triangle is 180°.

The measurements of the triangle are ∠A = (2x - 9)°, ∠B = (2x + 4)°, and ∠C = x°.

Equation: (2x - 9) + (2x + 4) + x = 180

Step 1: Combine like terms.

$\implies 2x + 2x + x- 9 + 4 = 180$

$\implies 5x - 5 = 180$

Step 2: Add 5 to both sides.

$\implies 5x - 5 + 5 = 180 + 5$

$\implies 5x = 185$

Step 3: Divide both sides by 5.

$\implies (5x)/(5) = (185)/(5)$

$\implies x = 37$

Step 4: Substitute 37 as the value of x in ∠A, ∠B, and ∠C to find their measures.

$\angle {\sf A} \implies 2(37) - 9 = 65$

$\angle {\sf B} \implies 2(37) + 4 = 78$

$\angle {\sf C} \implies 37$

The measure of the angles are: ∠A = 65°, ∠B = 78°, and ∠C = 37° . Together, they add up to 180°.