Question

GEOMETRY 50POINTS!!!​

Answer 1

Hello!

HMK = 180° (flat angle)

so LMK

= HMK - HML

= 180° - 102°

= 78°

LMI = 180° (flat angle)

so IMJ

= LMI - (KMJ + LMK)

= 180° - (50° + 78°)

= 52°

HMK = 180° (flat angle)

so HMI

= HMK - (IMJ + JMK)

= 180° - (52° + 50°)

= 78°

Conclusion :

JMH

= HMI + IMJ

= 78° + 52°

= 130°

The answer is 130°.

Answer 2

ᶻz !! Given !! ␥

• ∠LMH = 102°
• ∠KMJ = 50°

ㅤ

ᶻz !! To Find !! ␥

• ∠JMH

ㅤ

ᶻz !! Solution !! ␥

`\begin{gathered} \\ \\ \; :\implies \; \tt{\angle{LMH} + \angle{IMH} = 180^(\circ)} \qquad \bigg \lgroup{\sf{Linear \: Pair}\bigg \rgroup} \\ \\ \end{gathered}`

`\begin{gathered} \; :\implies \; \tt{102^(\circ) + \angle{IMH} = 180^(\circ)} \\ \\ \end{gathered}`

`\begin{gathered} \; :\implies \; \tt{\angle{IMH} = 180^(\circ) - 102^(\circ)} \\ \\ \end{gathered}`

`\begin{gathered} \; :\implies \; \tt{\angle{IMH} = 78^(\circ)} \\ \\ \end{gathered}`

`\begin{gathered} \\ \\ \; :\implies \; \tt{\angle{KMJ} + \angle{JMI} + \angle{IMH} = 180^(\circ)} \qquad \bigg \lgroup{\sf{Linear \: Pair}\bigg \rgroup} \\ \\ \end{gathered}`

`\begin{gathered} \; :\implies \; \tt{50^(\circ) + \angle{JMI} + 78^(\circ) = 180^(\circ)} \\ \\ \end{gathered}`

`\begin{gathered} \; :\implies \; \tt{\angle{JMI} + 78^(\circ) + 50^(\circ) = 180^(\circ)} \\ \\ \end{gathered}`

`\begin{gathered} \; :\implies \; \tt{\angle{JMI} + 128^(\circ) = 180^(\circ)} \\ \\ \end{gathered}`

`\begin{gathered} \; :\implies \; \tt{\angle{JMI} = 180^(\circ) - 128^(\circ)} \\ \\ \end{gathered}`

`\begin{gathered} \; :\implies \; \tt{\angle{JMI} = 52^(\circ)} \\ \\ \end{gathered}`

`\begin{gathered} \\ \\ \; :\implies \; \tt{\angle{JMH} = \angle{JMI} + \angle{IMH}} \\ \\ \end{gathered}`

`\begin{gathered} \; :\implies \; \tt{\angle{JMH} = 52^(\circ) + 78^(\circ)} \\ \\ \end{gathered}`

`\begin{gathered} \; :\implies \; \underline{\boxed{\tt{\angle{JMH} = 130^(\circ)}}} \; \pmb{\bigstar} \\ \\ \end{gathered}`