Question

In the triangle below, suppose that mZL=(x+3)°, mZ M=(5x-7)°, and m N= (2x).
Find the degree measure of each angle in the triangle.
N
(2x)
mL =
日。
х
M
(5x - 7).
m M =
•
•
mZN =
(x + 3)°

Answer 1

Answer:

Given

Triangle ABC is right angled at A.

$m\angle B=(5x+7)^∠B=(5x+7)∘$

$m\angleC=(4x+29)^∠C=(4x+29)$

To find:

The degree measure of each angle in the triangle.

Solution:

According to the given information,

$m\angleA=90^\circm∠A=90$

$m\angleB=(5x+7)^\circm∠B=(5x+7)$

$m\angleC=(4x+29)^\circm∠C=(4x+29) ∘$

Now,

$m\angleA+m\angleB+m\angleC=180^\circm∠A+m∠B+m∠C=180 ∘$

(Angle sum property)

$90^\circ+(5x+7)^\circ+(4x+29)^\circ=180^\circ90∘+(5x+7)∘+(4x+29) ∘ =180$∘

$(9x+126)^\circ=180^\circ(9x+126)∘ =180∘$

9x+126=1809x+126=180

9x=180-1269x=180−126

9x=549x=54

Divide both sides by 9.

$\sf{x=\dfrac{54}{9}x=954}$

x=6x=6

Now,

$m\angle A=90^\circm∠A=90

∘$

$m\angleB=(5(6)+7)^\circm∠B=(5(6)+7)$

∘

$m\angle B=37^\circm∠B=37$

∘

$m\angleC=(4(6)+29)^\circm∠C=(4(6)+29)$

∘

$m\angle C=53^\circum \: ∠C=53$

Therefore,

The measures of ∠A, ∠B, ∠C are 90°, 37°, 53° respectively.

Answer 2

Answer:

• 26°, 108°, 46°

Step-by-step explanation:

Assumed the given is:

• ΔLMN with angle measures of (x + 3), (5x - 7) and 2x.

We need to find the angle measures in degrees.

We know the sum of interior angles is 180:

• x + 3 + 5x - 7 + 2x = 180
• 8x - 4 = 180
• 8x = 184
• x = 184/8
• x = 23

Find the angle measures:

• m∠L = x + 3 = 23 + 3 = 26
• m∠M = 5x - 7 = 5*23 - 7 = 108
• m∠N = 2x = 2*23 = 46