Question

Use the information given in the following С figure to find : a= 90° b= 2x+4° c = 3x-5°. d= 8x-15°​

Answer 1

Step-by-step explanation:

Given :

∠A = Perpendicular = 90°

∠B = 2x + 4°

∠C = 3x - 5°

∠D = 8x - 15°

To find :

x

∠B and ∠C

Solution :

We know that,

The sum of the measures of angles of quadrilateral is 360°

As, according to the question,

\begin{gathered} \displaystyle\implies{ \rm \angle A + \angle B + \angle C + \angle D = 360 \degree} \\ \implies { \rm90 \degree + (2x + 4 ) \degree+ (3x - 5 )\degree+ (8x - 15 )\degree= 360 \degree} \\ \implies{ \rm90 + 2x + 4 \: + 3x - 5 + 8x - 15 = 360 \degree} \\ \implies { \rm13x + 74 \degree = 360 \degree} \\ \implies { \rm13x = 360 - 74} \\ \implies{ \rm 13x = 286 \degree} \\ \implies { \rm \: x = \frac{286}{13} } \\ \implies \boxed { \red {x = 22 \degree}}\end{gathered}

⟹∠A+∠B+∠C+∠D=360°

⟹90°+(2x+4)°+(3x−5)°+(8x−15)°=360°

⟹90+2x+4+3x−5+8x−15=360°

⟹13x+74°=360°

⟹13x=360−74

⟹13x=286°

⟹x=

13

286

⟹

x=22°

Measure of ∠B = 2x + 4

= 2(22) + 4

= 44 + 4

= 48°

Measure of ∠C = 3x - 5°

= 3(22) - 5

= 66 - 5

= 61°

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